diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..7a3811f --- /dev/null +++ b/.gitignore @@ -0,0 +1,9 @@ +!.gitignore +.DS_Store +**/.DS_Store +*.pyc +**/*.pyc +**/__pycache__ +**/*.egg-info +build +dist \ No newline at end of file diff --git a/Examples/Test_SLIT.py b/Examples/Test_SLIT.py index 1e76311..501ba62 100644 --- a/Examples/Test_SLIT.py +++ b/Examples/Test_SLIT.py @@ -1,9 +1,10 @@ -import pyfits as pf +import astropy.io.fits as pf import matplotlib.pyplot as plt import numpy as np import matplotlib.cm as cm -import SLIT +import SLIT.Solve +import SLIT.Lens import time from scipy import signal as scp import warnings @@ -75,17 +76,18 @@ def SIE(x0,y0,n1,n2,b,beta,q,xc,theta): ################################Running SLIT############################ #Parameters kmax = 5 -niter =100 +niter = 100 levels = [0] #Comment the following to have the level estimation routine run (takes more time) -levels = pf.open('../Files/Noise_levels_SLIT.fits')[0].data +# levels = pf.open('../Files/Noise_levels_SLIT.fits')[0].data #Start clock start = time.clock() #Running SLIT -sourcesl, Imsl = SLIT.SLIT(Image, Fkappa, kmax, niter, size, PSF, PSFconj, levels = levels, fb =1) +sourcesl, Imsl, Res1, Res2, sigma0 = SLIT.Solve.SLIT(Image, Fkappa, kmax, niter, size, PSF, PSFconj, + levels=levels, scheme='FB', show_plots=True) #Stop clock elapsed = (time.clock()-start) @@ -110,25 +112,33 @@ def SIE(x0,y0,n1,n2,b,beta,q,xc,theta): plt.imshow((sourcesl), vmin = np.min(real_source), vmax = np.max(real_source),cmap = cm.gist_stern, interpolation = 'nearest') plt.axis('off') plt.colorbar() + plt.savefig("Test_SLIT_fig2.png") + plt.close() # plt.subplot(2,3,2) plt.figure(3) plt.title('Original source') plt.imshow(real_source, cmap = cm.gist_stern, interpolation = 'nearest') plt.axis('off') plt.colorbar() + plt.savefig("Test_SLIT_fig3.png") + plt.close() # plt.subplot(2,3,3) plt.figure(4) plt.title('Lensed source') plt.imshow(Image, cmap = cm.gist_stern, interpolation = 'nearest') plt.axis('off') plt.colorbar() - plt.figure(41) + plt.savefig("Test_SLIT_fig4.png") + plt.close() + plt.figure(5) plt.title('Reconstructed lensed source') plt.imshow(Imsl, vmin = np.min(Image), vmax = np.max(Image), cmap = cm.gist_stern, interpolation = 'nearest') plt.axis('off') plt.colorbar() - # plt.subplot(2,3,4) - plt.figure(5) + plt.savefig("Test_SLIT_fig5.png") + plt.close() +# plt.subplot(2,3,4) + plt.figure(6) plt.title('relative difference') diff = (real_source-sourcesl)/real_source diff[np.where(real_source==0)] = 0 @@ -136,16 +146,22 @@ def SIE(x0,y0,n1,n2,b,beta,q,xc,theta): plt.imshow(np.abs(diff), vmax = 1., vmin = 0., cmap = cm.gist_stern, interpolation = 'nearest' ) plt.axis('off') plt.colorbar() + plt.savefig("Test_SLIT_fig6.png") + plt.close() # plt.subplot(2,3,5) - plt.figure(6) + plt.figure(7) plt.title('difference with reconstructed lensed image') plt.imshow(Image-Imsl, vmin = -5*sigma, vmax = 5*sigma, cmap = cm.gist_stern, interpolation = 'nearest') plt.axis('off') plt.colorbar() + plt.savefig("Test_SLIT_fig7.png") + plt.close() # plt.subplot(2,3,6) - plt.figure(7) + plt.figure(8) plt.title('difference with true source') plt.imshow((np.abs(real_source-sourcesl)), cmap = cm.gist_stern, interpolation = 'nearest') plt.axis('off') plt.colorbar() -plt.show() + plt.savefig("Test_SLIT_fig8.png") + plt.close() +# plt.show() diff --git a/Examples/Test_SLIT_MCA.py b/Examples/Test_SLIT_MCA.py index 23f9a45..cecd6c0 100644 --- a/Examples/Test_SLIT_MCA.py +++ b/Examples/Test_SLIT_MCA.py @@ -1,5 +1,6 @@ from SLIT import Lens -import pyfits as pf +# import pyfits as pf +import astropy.io.fits as pf import matplotlib.pyplot as plt import numpy as np import matplotlib.cm as cm diff --git a/Files/.DS_Store b/Files/.DS_Store new file mode 100644 index 0000000..5008ddf Binary files /dev/null and b/Files/.DS_Store differ diff --git a/Results_center/Image_0_0.0_3.07609150209.fits b/Results_center/Image_0_0.0_3.07609150209.fits deleted file mode 100644 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a/Results_slope/Source_9_2.1.fits b/Results_slope/Source_9_2.1.fits deleted file mode 100644 index fe1c977..0000000 Binary files a/Results_slope/Source_9_2.1.fits and /dev/null differ diff --git a/Results_slope/alphax_PL_true.fits b/Results_slope/alphax_PL_true.fits deleted file mode 100644 index c0dcd14..0000000 Binary files a/Results_slope/alphax_PL_true.fits and /dev/null differ diff --git a/Results_slope/alphay_PL_true.fits b/Results_slope/alphay_PL_true.fits deleted file mode 100644 index 78a365e..0000000 Binary files a/Results_slope/alphay_PL_true.fits and /dev/null differ diff --git a/SLIT.egg-info/PKG-INFO b/SLIT.egg-info/PKG-INFO deleted file mode 100644 index d9cac16..0000000 --- a/SLIT.egg-info/PKG-INFO +++ /dev/null @@ -1,10 +0,0 @@ -Metadata-Version: 1.0 -Name: SLIT -Version: 0.1 -Summary: Code for colour lens/source separation and lensed source reconstruction -Home-page: UNKNOWN -Author: Remy Joseph, Frederic Courbin, Jean-Luc Starck -Author-email: remy.joseph@epfl.ch -License: UNKNOWN -Description: UNKNOWN -Platform: UNKNOWN diff --git a/SLIT.egg-info/SOURCES.txt b/SLIT.egg-info/SOURCES.txt deleted file mode 100644 index 753cba5..0000000 --- a/SLIT.egg-info/SOURCES.txt +++ /dev/null @@ -1,11 +0,0 @@ -setup.py -SLIT/Lens.py -SLIT/Solve.py -SLIT/__init__.py -SLIT/tools.py -SLIT/wave_transform.py -SLIT.egg-info/PKG-INFO -SLIT.egg-info/SOURCES.txt -SLIT.egg-info/dependency_links.txt -SLIT.egg-info/not-zip-safe -SLIT.egg-info/top_level.txt \ No newline at end of file diff --git a/SLIT.egg-info/dependency_links.txt b/SLIT.egg-info/dependency_links.txt deleted file mode 100644 index 8b13789..0000000 --- a/SLIT.egg-info/dependency_links.txt +++ /dev/null @@ -1 +0,0 @@ - diff --git a/SLIT.egg-info/not-zip-safe b/SLIT.egg-info/not-zip-safe deleted file mode 100644 index 8b13789..0000000 --- a/SLIT.egg-info/not-zip-safe +++ /dev/null @@ -1 +0,0 @@ - diff --git a/SLIT.egg-info/top_level.txt b/SLIT.egg-info/top_level.txt deleted file mode 100644 index dea0630..0000000 --- a/SLIT.egg-info/top_level.txt +++ /dev/null @@ -1 +0,0 @@ -SLIT diff --git a/SLIT/.DS_Store b/SLIT/.DS_Store new file mode 100644 index 0000000..5008ddf Binary files /dev/null and b/SLIT/.DS_Store differ diff --git a/SLIT/Lens.py b/SLIT/Lens.py index 6330788..a230f7b 100755 --- a/SLIT/Lens.py +++ b/SLIT/Lens.py @@ -1,6 +1,6 @@ import numpy as np import matplotlib.pyplot as plt -import pyfits as pf +import astropy.io.fits as pf import scipy.signal as scp import warnings warnings.simplefilter("ignore") @@ -13,11 +13,25 @@ def SIS(x0,y0,n1,n2,Re): count = 0 for i in x: kappa[x[count],y[count]] = Re/(2*np.sqrt((x[count]-x0)**2+(y[count]-y0)**2)) - count += 1 if np.isfinite(kappa[x0,y0]) == False: kappa[x0,y0] = 1 - + + return kappa + +def Power_law_xy(x,y,x0,y0,k0,theta,q,gamma,rc): + up = k0*(2-gamma/2.)*q**(gamma-3./2.) + theta = theta*np.pi/180. + Xr = (x-x0)*np.cos(theta)-(y-y0)*np.sin(theta) + Yr = (x-x0)*np.sin(theta)+(y-y0)*np.cos(theta) + down = 2*(q**2*((Xr)**2+rc**2)+Yr**2)**(0.5*(gamma-1)) + return up/down + +def Power_law(x0,y0,n1,n2,k0,theta,q,gamma, rc): + x,y = np.where(np.zeros((n1,n2))==0) + X = np.reshape(x, (n1,n2)) + Y = np.reshape(y, (n1,n2)) + kappa = Power_law_xy(X,Y,x0,y0,k0,theta,q,gamma, rc) return kappa def SIE_xy(x,y,x0,y0,b,beta,q,xc,theta): @@ -29,7 +43,6 @@ def SIE_xy(x,y,x0,y0,b,beta,q,xc,theta): Xr = (x-x0)*np.cos(theta)-(y-y0)*np.sin(theta) Yr = (x-x0)*np.sin(theta)+(y-y0)*np.cos(theta) kappa = pre/((xc**2.)/(1.-eps)+(Xr)**2.+((Yr)**2.)/q**2.)**((beta-1.)/2.) - return kappa def SIE(x0,y0,n1,n2,b,beta,q,xc,theta): @@ -40,41 +53,71 @@ def SIE(x0,y0,n1,n2,b,beta,q,xc,theta): kappa = SIE_xy(x2d,y2d,x0,y0,b,beta,q,xc,theta) return kappa +def shear(kappa, n1,n2): + nk1, nk2 = np.shape(kappa) + # Coordonnees de la grille de l'espace image + [x, y] = np.where(np.zeros([nk1, nk2]) == 0) + + x0 = nk1 / 2 + y0 = nk2 / 2 + + xc = np.reshape((x) - x0, (nk1, nk2)) + yc = np.reshape((y) - y0, (nk1, nk2)) -def alpha_def(kappa, n1,n2,extra=0): - #Computes the deflection angle of a single photon at coordinates theta in the source plane and a lens + r = (xc ** 2 + yc ** 2)**2 + Real = xc**2-yc**2 + Ima = -2*xc*yc + lx, ly = np.where(r == 0) + tabReal = np.reshape(np.float_(Real) / (r), (nk1, nk2)) + tabIma = np.reshape(np.float_(Ima) / (r), (nk1, nk2)) + tabReal[lx, ly] = 0 + tabIma[lx, ly] = 0 + + kappa = kappa.astype(float) + tabReal = tabReal.astype(float) + tabIma = tabIma.astype(float) + # kappa[rk>(nk1)/2.] = 0 + + gamma1 = scp.fftconvolve(tabReal, (kappa), mode='same') / np.pi + gamma2 = scp.fftconvolve(tabIma, (kappa), mode='same') / np.pi + + return gamma1, gamma2 + +def Jacobian_det(kappa, n1,n2): + gamma1, gamma2 = shear(kappa, n1,n2) + det = 1./((1-kappa)**2-(gamma1**2+gamma2**2)) + + return det + +def alpha_def(kappa, n1, n2): + #Computes the deflection angle of a single photon at coordinates theta in the source plane and a lens #mass distribution kappa - - nk1,nk2 = np.shape(kappa) + + nk1, nk2 = np.shape(kappa) + #Coordonnees de la grille de l'espace image - [x,y] = np.where(np.zeros([nk1,nk2])==0) + x, y = np.where(np.zeros([nk1, nk2]) == 0) x0 = nk1/2 y0 = nk2/2 + xc = np.reshape(x - x0, (nk1, nk2)).astype(float) + yc = np.reshape(y - y0, (nk1, nk2)).astype(float) - xc = np.reshape((x)-x0,(nk1,nk2)) - yc = np.reshape((y)-y0,(nk1,nk2)) - - - - r = (xc**2+yc**2) - lx,ly = np.where(r==0) - tabx = np.reshape(np.float_(xc)/(r),(nk1,nk2)) - taby = np.reshape(np.float_(yc)/(r),(nk1,nk2)) - tabx[lx,ly]=0 - taby[lx,ly]=0 - - kappa = kappa.astype(float) - tabx = tabx.astype(float) + r2 = (xc**2 + yc**2) + lx, ly = np.where(r2 == 0) + tabx = np.reshape(xc / r2, (nk1, nk2)) + taby = np.reshape(yc / r2, (nk1, nk2)) + tabx[lx, ly] = 0 + taby[lx, ly] = 0 # kappa[rk>(nk1)/2.] = 0 - - intex = scp.fftconvolve(tabx, (kappa), mode = 'same')/np.pi - intey = scp.fftconvolve(taby, (kappa), mode = 'same')/np.pi - return intex[x0-(n1)/2:x0+(n1)/2,y0-(n2)/2:y0+(n2)/2], intey[x0-(n1)/2:x0+(n1)/2,y0-(n2)/2:y0+(n2)/2] + intex = scp.fftconvolve(tabx, kappa, mode='same') / np.pi + intey = scp.fftconvolve(taby, kappa, mode='same') / np.pi + return intex[int(x0-n1/2):int(x0+n1/2), int(y0-n2/2):int(y0+n2/2)], \ + intey[int(x0-n1/2):int(x0+n1/2), int(y0-n2/2):int(y0+n2/2)] def beta(kappa,theta): #Computes beta @@ -86,93 +129,80 @@ def theta(alpha, beta): theta = beta+alpha return beta -def F(kappa, nt1,nt2, size, extra=100, x_shear = 0, y_shear = 0, alpha_x_in = [-99], alpha_y_in = [-99]): +def F(kappa, nt1, nt2, size, x_shear=0, y_shear=0, alpha_x_in=None, alpha_y_in=None): # Theta positions for each pixel in beta - if np.sum(alpha_x_in) != [-99]: + if (alpha_x_in is not None) and (alpha_y_in is not None): + print("Deflection angles have been provided") alpha_x = alpha_x_in alpha_y = alpha_y_in else: + alpha_x, alpha_y = alpha_def(kappa, nt1, nt2) - nk1,nk2 = np.shape(kappa) - - alpha_x,alpha_y = alpha_def(kappa,nt1,nt2,extra = extra) - - - alpha_x = alpha_x+x_shear - alpha_y = alpha_y+y_shear - + alpha_x = alpha_x + x_shear + alpha_y = alpha_y + y_shear - na1,na2 = np.shape(alpha_x) - xa,ya = np.where(np.zeros((na1,na2)) == 0) + na1, na2 = np.shape(alpha_x) + xa, ya = np.where(np.zeros((na1, na2)) == 0) - - nb1=nt1*size - nb2=nt2*size - xb, yb = np.where(np.zeros((nb1,nb2))==0) + nb1 = int(nt1*size) + nb2 = int(nt2*size) + xb, yb = np.where(np.zeros((nb1, nb2)) == 0) #Scaling of the source grid - - #Scaling of the deflection grid - xa = xa*(np.float(nt1)/np.float(na1))#-0.68 - ya = ya*(np.float(nt2)/np.float(na2))#-0.68 - #Setting images coordinates in 2d - xa2d = np.reshape(xa,(na1,na2)) - ya2d = np.reshape(ya,(na1,na2)) + #Scaling of the deflection grid + xa = xa * float(nt1) / float(na1) + ya = ya * float(nt2) / float(na2) + #Setting images coordinates in 2d + xa2d = np.reshape(xa, (na1, na2)) + ya2d = np.reshape(ya, (na1, na2)) - F2 = [] + F2 = [] # TODO : try multiprocessing for the loop below for i in range(np.size(xb)): #Deflection of photons emitted in xb[i],yb[i] - theta_x = (xb[i])*(np.float(nt1)/np.float(nb1))+alpha_x - theta_y = (yb[i])*(np.float(nt2)/np.float(nb2))+alpha_y + theta_x = xb[i] * float(nt1) / float(nb1) + alpha_x + theta_y = yb[i] * float(nt2) / float(nb2) + alpha_y #Matching of arrivals with pixels in image plane - xprox = np.int_(np.abs((xa2d-theta_x)*2)) - yprox = np.int_(np.abs((ya2d-theta_y)*2)) + xprox = np.int_(np.abs((xa2d - theta_x) * 2)) + yprox = np.int_(np.abs((ya2d - theta_y) * 2)) - - if np.min(xprox+yprox) <1: - loc2 = np.array(np.where((xprox+yprox)==np.min(xprox+yprox)))*np.float(nt1)/np.float(na1)# + if np.min(xprox + yprox) == 0: + loc2 = np.array(np.where((xprox + yprox) == 0)) #* float(nt1) / float(na1) because always 1 ;) + loc2_pix = np.int_(loc2) else: - loc2 = [] - if (np.size(loc2)==0): + loc2_pix = None + + F2.append(loc2_pix) - F2.append([0]) - else: - F2.append(np.int_(loc2)) return F2 -def source_to_image(Source, nt1,nt2, theta, ones = 1): +def source_to_image(Source, nt1,nt2, theta, ones=1): # Source: Image of the source in the source plane # n1,n2: size in pixels of the postage stamp in image plane # F: the coordinates of the lens mapping - F = (theta) - nb1,nb2 = np.shape(Source) + F = theta + nb1, nb2 = np.shape(Source) if ones == 1: - onelens = source_to_image(np.ones(Source.shape), nt1,nt2, theta, ones = 0) - onelens[np.where(onelens==0)]=1 - + onelens = source_to_image(np.ones(Source.shape), nt1, nt2, theta, ones=0) + onelens[np.where(onelens == 0)] = 1 else: onelens = 1. - Image = np.zeros((nt1,nt2)) - xb,yb = np.where(np.zeros((nb1,nb2)) == 0) + xb, yb = np.where(np.zeros((nb1,nb2)) == 0) N = np.size(xb) - k=0 - for pos in F: - - if np.size(np.shape(pos)) != 1: - - Image[np.array(pos[0][:]), - np.array(pos[1][:])] += Source[xb[k],yb[k]]#fullSource - k=k+1 + for k, pos in enumerate(F): + if pos is not None: + Image[np.array(pos[0][:]), + np.array(pos[1][:])] += Source[xb[k], yb[k]] #fullSource + return Image/onelens @@ -181,28 +211,30 @@ def image_to_source(Image, size,beta,lensed = 0, square = 0): # nsize1,nsize2: size of the postagestamp in source plane # F: lens mapping matrix - F = (beta) + F = beta nt1,nt2 = np.shape(Image) - nb1 = nt1*size - nb2 = nt2*size + nb1 = int(nt1*size) + nb2 = int(nt2*size) Source = np.zeros((nb1,nb2)) xb,yb = np.where(Source == 0) N = np.size(xb) - - for k in range(N): - pos = F[k] - if np.size(np.shape(pos)) > 1: - if np.sum(lensed) !=0: - if square == 0: - Source[xb[k],yb[k]] += np.sum(Image[np.array(pos[0][:]), - np.array(pos[1][:])])/np.max([1,np.size(pos[0][:])]) - else: - Source[xb[k], yb[k]] += np.sum((Image[np.array(pos[0][:]), - np.array(pos[1][:])] / np.max([1, np.size(pos[0][:])]))**2) - else: - Source[xb[k],yb[k]] += np.sum(Image[np.array(pos[0][:]), - np.array(pos[1][:])]) + + for k, pos in enumerate(F): + + if pos is not None: + + light = Image[np.array(pos[0][:]), np.array(pos[1][:])] + + if np.sum(lensed) != 0: + light /= np.max([1, np.size(pos[0][:])]) + if square == 1: + Source[xb[k], yb[k]] += np.sum(light**2) + else: + Source[xb[k], yb[k]] += np.sum(light) + else: + Source[xb[k],yb[k]] += np.sum(light) + if square == 1: Source = np.sqrt(Source) return Source @@ -212,22 +244,22 @@ def image_to_source_bound(Image, size,beta,lensed = 0): # nsize1,nsize2: size of the postagestamp in source plane # F: lens mapping matrix - F = (beta) + F = beta nt1,nt2 = np.shape(Image) - nb1 = nt1*size - nb2 = nt2*size + nb1 = int(nt1*size) + nb2 = int(nt2*size) Source = np.zeros((nb1,nb2)) xb,yb = np.where(Source == 0) N = np.size(xb) for k in range(N): - pos = F[k] - if np.size(np.shape(pos)) > 1: - if np.sum(lensed) !=0: - Source[xb[k],yb[k]] += np.sum(Image[np.array(pos[0][:]), - np.array(pos[1][:])])/np.max([1,np.size(pos[0][:])]) - else: - Source[xb[k],yb[k]] += np.sum(Image[np.array(pos[0][:]), - np.array(pos[1][:])]) - + pos = F[k] + if pos is not None: + if np.sum(lensed) !=0: + Source[xb[k],yb[k]] += np.sum(Image[np.array(pos[0][:]), + np.array(pos[1][:])])/np.max([1,np.size(pos[0][:])]) + else: + Source[xb[k],yb[k]] += np.sum(Image[np.array(pos[0][:]), + np.array(pos[1][:])]) + return Source diff --git a/SLIT/Lens.pyc b/SLIT/Lens.pyc deleted file mode 100644 index 3bbab52..0000000 Binary files a/SLIT/Lens.pyc and /dev/null differ diff --git a/SLIT/Solve.py b/SLIT/Solve.py index dbbce5e..798f5b7 100755 --- a/SLIT/Solve.py +++ b/SLIT/Solve.py @@ -1,24 +1,26 @@ #from __future__ import division -import wave_transform as mw import numpy as np import matplotlib.pyplot as plt -import pyfits as pf +import astropy.io.fits as pf import matplotlib.cm as cm +import warnings +import multiprocess as mtp +from numpy import linalg as LA from scipy import signal as scp import scipy.ndimage.filters as med -import MuSCADeT as wine -from numpy import linalg as LA -import multiprocess as mtp -from pathos.multiprocessing import ProcessingPool as Pool -import Lens -import warnings -import tools +import time + +from SLIT import Lens +from SLIT import tools + + warnings.simplefilter("ignore") ##SLIT: Sparse Lens Inversion Technique -def SLIT(Y, Fkappa, kmax, niter, size, PSF, PSFconj, S0 = [0], levels = [0], scheme = 'FB', - mask = [0], lvl = 0, weightS = 1, noise = 'gaussian', tau = 0, verbosity = 0): +def SLIT(input_image, Fkappa, kmax, niter, size, PSF, PSFconj, S0 = [0], levels = [0], scheme = 'FB', + mask = [0], lvl = 0, weightS = 1, noise = 'gaussian', tau = 0, verbosity = 0, nweights = 1, + noise_levels_file='Noise_levels.fits', save_steps_dir=None, show_plots=False): ##DESCRIPTION: ## Function that estimates the source light profile from an image of a lensed source given the mass density profile. ## @@ -49,17 +51,19 @@ def SLIT(Y, Fkappa, kmax, niter, size, PSF, PSFconj, S0 = [0], levels = [0], sch ##EXAMPLE: ## S,FS = SLIT(img, Fkappa, 5, 100, 1, PSF, PSFconj) - n1,n2 = np.shape(Y) + n1,n2 = np.shape(input_image) PSFconj = PSF.T #Size of the source - ns1,ns2 = n1*size, n2*size + ns1,ns2 = int(n1*size), int(n2*size) #Number of starlet scales in source plane - if lvl ==0: - lvl = np.int(np.log2(ns2)) + if lvl == 0: + lvl = int(np.log2(ns2)) else: lvl = np.min([lvl,np.int(np.log2(ns2))]) - lvlg = np.int(np.log2(n2)) + print("number of starlet scales ('lvl') :", lvl) + + lvlg = int(np.log2(n2)) #Masking if required if np.sum(mask) == 0: mask = np.ones((n1,n2)) @@ -67,25 +71,41 @@ def SLIT(Y, Fkappa, kmax, niter, size, PSF, PSFconj, S0 = [0], levels = [0], sch #Noise in image plane if noise == 'gaussian': - print('noise statistic is gaussain') - sigma0 = tools.MAD(Y) + print('noise statistic is gaussian') + sigma0 = tools.MAD(input_image) print('sigma: ', sigma0) if noise == 'poisson': print('noise statistic is poisson') - sigma0 = tools.MAD_poisson(Y,tau) + sigma0 = tools.MAD_poisson(input_image,tau) if (noise == 'G+P') or (noise == 'P+G'): - print('noise statistic is poisson and gaussain mixture') - sigma0 = np.sqrt(tools.MAD_poisson(Y,tau, lvlg)**2+tools.MAD(Y)**2) - - - plt.imshow(sigma0); plt.colorbar(); plt.show() - - #Mapping of an all-at-one image to source plane + print('noise statistic is poisson and gaussian mixture') + sigma0 = np.sqrt(tools.MAD_poisson(input_image,tau, lvlg)**2+tools.MAD(input_image)**2) + plt.imshow(sigma0, origin='lower'); plt.colorbar(); plt.show() + + # replace masked pixels with gaussian noise (fix k computation) + masked_pixels = np.where(mask == 0) + gaussian_noise_map = sigma0 * np.random.randn(n1, n2) + Y = np.copy(input_image) + Y[masked_pixels] = gaussian_noise_map[masked_pixels] + + if show_plots: + plt.figure() + plt.imshow(Y, origin='lower') + plt.title("input") + + #Mapping of an all-at-one image to source plane (does not take a lot of time) lensed = lens_one(Fkappa, n1,n2, size) + #estimation of the frame of the image in source plane supp = np.zeros((lvl,lensed.shape[0],lensed.shape[1])) - supp[:,lensed/lensed ==1] =1 - supp = 1 + supp[:, lensed/lensed==1] = 1 + + #Limits of the image plane in source plane + bound = mk_bound(Fkappa, n1,n2, size) + if show_plots: + plt.figure() + plt.imshow(bound, origin='lower') + plt.title("bounds in source plane") #Useful functions def Finv_apply(I): @@ -99,9 +119,10 @@ def PSF_apply(i): def PSFT_apply(ii): return scp.fftconvolve(ii,PSFconj,mode = 'same') def transform(x): - return tools.wave_transform(x, lvl, newwave = 1) + coeffs, _ = tools.wave_transform(x, lvl, newwave=1) + return coeffs def inverse(x): - return tools.iuwt(x) + return tools.iuwt(x, newwave=1) #Forward operator def F_op(X): @@ -131,51 +152,51 @@ def reg_supp(X): return X*supp def reg_filter(X): return tools.mr_filter(X,levels,ks,10,transform, inverse, I_op(sigma0*np.ones((n1,n2))), lvl = lvl, supp = supp) - #Noise simulations to estimate noise levels in source plane - if np.sum(levels)==0: + + ## Noise simulations to estimate noise levels in source plane + if not np.any(levels): print('Calculating noise levels') #levels = simulate_noise(n1,n2, sigma0, size, I_op, transform, lvl) - levels = level_source(n1,n2,sigma0,size,PSFconj, Lens_op2, lensed, lvl) + levels = level_source(n1, n2, sigma0, size, PSFconj, Lens_op2, lensed, lvl) #Saves levels hdus = pf.PrimaryHDU(levels) lists = pf.HDUList([hdus]) - lists.writeto('Noise_levels.fits', clobber=True) - + lists.writeto(noise_levels_file, clobber=True) + def mk_levels(sigma): return level_source(n1,n2,sigma0,size,PSFconj, Lens_op2, lensed, lvl) -##Compute spectral norms - opwave_norm = spectralNorm(n1,n2,20,1e-10,IW_op,FW_op) - op_norm = spectralNorm(ns1, ns2, 20, 1e-10, F_op, I_op) - wave_norm = spectralNorm(ns1,ns2,20,1e-10,transform,inverse) + ## Compute spectral norms (takes A LOT of time) if scheme == 'Vu': + op_norm = spectralNorm(ns1, ns2, 20, 1e-10, F_op, I_op) + wave_norm = spectralNorm(ns1,ns2,20,1e-10,transform,inverse) mu = 1. tau = 1./(mu*wave_norm**2+0.5*op_norm) if verbosity == 1: print(mu,tau) else: + opwave_norm = spectralNorm(n1,n2,20,1e-10,IW_op,FW_op) mu = .5/(opwave_norm) if verbosity == 1: print(mu) - if (scheme == 'FISTA'): - repeat = 2 - elif (scheme == 'Vu'): - repeat = 1 - else: - repeat = 1 - #Initialisation - - Res1= [] + ## Initialisation + niter0 = np.copy(niter) + Res1 = [] + steps_to_save = [] + for jr in range(nweights): + if jr!= nweights-1: + niter = niter0 #/2 + else: + niter = niter0 - for jr in range(repeat): trans = (transform(I_op(Y))/levels)*supp #trans[:,lensed==0] = 0 - trans[levels==0] =0 + trans[levels==0] = 0 ks0 = np.max(trans)*0.9 print(ks0) ks=np.copy(ks0) @@ -184,7 +205,6 @@ def mk_levels(sigma): i = 0 ts = 1 - csi = 0 M = [0] Res1= [] Res2 = [] @@ -195,83 +215,106 @@ def mk_levels(sigma): S = S0 Snew = S alpha =transform(S) + alphaY = transform(I_op(Y)) alphanew = np.copy(alpha) + csi = np.copy(alphanew) points = 0 - while i < niter: + while i < niter: if scheme == 'FB': - print('FB ', i) + if i % 10 == 0: + print('FB ', i) ks = ks0*np.exp(i*karg) ks = np.max([ks, kmax]) S = np.copy(Snew) Snew = tools.Forward_Backward(Y, S, F_op, I_op, transform, inverse, mu, reg1, pos = 1) - S[S<0] = 0 - FS = F_op(Snew)*mask + # S[S<0] = 0 # ORIGINAL CODE + Snew[Snew<0] = 0 + if (noise == 'G+P') or (noise == 'P+G') and (i<10): + FS = F_op(Snew)*mask sigma = (tools.MAD(Y)+np.sqrt(FS/tau)) levels = mk_levels(sigma) elif scheme == 'FISTA': - print('FISTA ', i) - S = np.copy(Snew) + if i % 10 == 0: + print('FISTA ', i) + + # S = np.copy(Snew) alphanew = np.copy(alpha) - alpha, csi, ts = tools.FISTA(Y, alphanew, F_op, I_op, mu, ts, csi, reg1, transform, inverse, mask = mask) + alpha, csi, ts = tools.FISTA(Y, alphanew, F_op, I_op, mu, ts, csi, reg1, transform, inverse, mask=mask) Snew = inverse(alpha) - FS = F_op(Snew) + #FS = F_op(Snew) + elif scheme == 'Vu': - print('Vu ', i) + if i % 10 == 0: + print('Vu ', i) S = np.copy(Snew) - Snew,alpha = tools.Vu_Primal_dual(Y, S, alpha, mu, tau, F_op, I_op, transform, inverse, reg1, reg_plus) - FS = F_op(Snew) - # plt.imshow(S) - # plt.show() + Snew, alpha = tools.Vu_Primal_dual(Y, S, alpha, mu, tau, F_op, I_op, transform, inverse, reg1, reg_plus) - + FS = F_op(Snew) + chi2 = tools.Res(Y, FS, sigma0) + SDR = tools.SDR(alpha, alphanew) - SDR = tools.SDR(alpha, alphanew) - Res = tools.Res(Y,FS,sigma0) #Convergence condition - Res1.append(Res) + Res1.append(chi2) Res2.append(SDR) + # ks = ks-steps if i>5: - add = Criteria(i, Res1, Res2) + add = Criteria(i, SDR, Res2) + if add == 0: points = np.max([0,points-1]) else: points+=add - if points >= 10: + + if points >= 5: print('BREAK: algorithm converged at iteration: ', i) break i = i+1 if i == niter: print('BREAK: Maximum number of iterations reached.') + + steps_to_save.append([Snew, FS, Y-FS]) # alpha = transform(S) - weightS = 1./(1.+np.exp(-10.*(levels*kmax-alpha))) -# plt.show() + + weightS = 2./(1.+np.exp(-10.*(levels*kmax-alpha))) + + Snew = inverse(alpha) + FS = F_op(Snew) + #Final reconstruction of the source if np.size(np.shape(sigma0))>2: sigma0[sigma0==0]=np.mean(sigma0) - if verbosity == 1: - plt.imshow((Y-FS)/(sigma0)); plt.colorbar(); plt.show() - plt.plot(Res1, 'b'); plt.show() + if show_plots: + plt.figure() + plt.imshow((Y-FS)/(sigma0), origin='lower'); plt.colorbar(); plt.show() plt.plot(Res2, 'r'); plt.show() + if noise == 'poisson': plt.subplot(211) plt.title('S') - plt.imshow(S); plt.colorbar() + plt.imshow(S, origin='lower'); plt.colorbar() plt.show() - return Snew, FS + + if save_steps_dir is not None: + print("Saving animation...") + tools.save_steps(save_steps_dir, steps_to_save, Y, suffix=scheme) + + return Snew, FS, Res1, Res2, sigma0 #############################SLIT MCA for blended lenses############################ -def SLIT_MCA(Y, Fkappa, kmax, niter, riter, size,PSF, PSFconj, lvlg = 0, lvls = 0, noise = 'gaussian', tau =0, levels = [0], WS = 1, WG = 1, mask = [0,0], Ginit=0, Kills = 0, Killg = 0): +def SLIT_MCA(input_image, Fkappa, kmax, niter, riter, size,PSF, PSFconj, lvlg = 0, lvls = 0, noise = 'gaussian', scheme = 'FISTA', decrease = 0, + tau =0, levels = [0], WS = 1, WG = 1, mask = [0,0], Sinit = 0, Ginit=0, Kills = 0, Killg = 0, verbosity = 0, nweight = 5, + noise_levels_file='Noise_levels_MCA.fits'): ##DESCRIPTION: ## Function that estimates the source and lens light profiles from an image of a ## strong lens system @@ -307,46 +350,69 @@ def SLIT_MCA(Y, Fkappa, kmax, niter, riter, size,PSF, PSFconj, lvlg = 0, lvls = ##EXAMPLE: ## S,FS = SLIT(img, Fkappa, 5, 100, 1, PSF, PSFconj) + niter = max([6, niter]) + #Shape of the image - n1,n2 = np.shape(Y) + n1, n2 = np.shape(input_image) #Initialisation of the source - ns1= n1*size - ns2 = n2*size + ns1 = int(n1*size) + ns2 = int(n2*size) PSFconj = PSF.T #Number of starlet scales in source and image planes - if lvlg ==0: - lvlg = np.int(np.log2(n2)) + if lvlg == 0: + lvlg = int(np.log2(n2)) else: - lvlg = np.min([lvlg,np.int(np.log2(n2))]) - lvls = lvlg - if lvls >np.int(np.log2(ns2)): - print('Error, too many wavelet levels for the source. Choose a smaller value for lvl') - exit + lvlg = np.min([lvlg, int(np.log2(n2))]) + + if lvls == 0: + lvls = int(np.log2(ns2)) + else: + lvls = np.min([lvls, int(np.log2(ns2))]) + + # lvls = lvlg + # if lvls > int(np.log2(ns2)): + # print('Error, too many wavelet levels for the source. Choose a smaller value for lvl') + # exit + #Masking if required if np.sum(mask) == 0: mask = np.ones((n1,n2)) - Y = Y*mask + + # input_image = input_image*mask # instead we put noise where pixels are masked + #Noise standard deviation in image plane if noise == 'gaussian': - print('noise statistic is gaussain') - sigma0 = tools.MAD(Y) + sigma0 = tools.MAD(input_image) + print('noise statistic is gaussian (sigma = {:.5e})'.format(sigma0)) if noise == 'poisson': - print('noise statistic is poisson') - sigma0 = tools.MAD_poisson(Y,tau) + sigma0 = tools.MAD_poisson(input_image, tau) + print('noise statistic is poisson (sigma = {:.5e})'.format(sigma0)) if (noise == 'G+P') or (noise == 'P+G'): - print('noise statistic is poisson and gaussain mixture') - sigma0 = np.sqrt(tools.MAD_poisson(Y,tau, lvlg)**2+tools.MAD(Y)**2) + sigma0 = np.sqrt(tools.MAD_poisson(input_image, tau, lvlg)**2 + tools.MAD(input_image)**2) + print('noise statistic is gaussian-poisson mixture (sigma = {:.3f})'.format(sigma0)) + + # replace masked pixels with gaussian noise (fix k computation) + masked_pixels = np.where(mask == 0) + gaussian_noise_map = sigma0 * np.random.randn(n1, n2) + + Y = np.copy(input_image) + Y[masked_pixels] = gaussian_noise_map[masked_pixels] + + plt.figure() + plt.imshow(Y, origin='lower') + plt.title("input") #Mapping of an all-at-one image lensed = lens_one(Fkappa, n1,n2, size) - supp = np.zeros((lvls,lensed.shape[0],lensed.shape[1])) supp[:,lensed/lensed ==1] =1 #Limits of the image plane in source plane bound = mk_bound(Fkappa, n1,n2, size) - + plt.figure() + plt.imshow(bound, origin='lower') + plt.title("bounds in source plane") #Useful functions @@ -361,9 +427,21 @@ def PSF_apply(i): def PSFT_apply(ii): return scp.fftconvolve(ii,PSFconj,mode = 'same') def transform(x): - return tools.wave_transform(x, lvlg) + coeffs, _ = tools.wave_transform(x, lvlg, newwave=1) + return coeffs def inverse(x): - return tools.iuwt(x) + return tools.iuwt(x, newwave=1) + + def FWS_op(X): + return PSF_apply(F_apply(inverse(X))) + #Inverse operator + def IWS_op(X): + return transform(Finv_apply(PSFT_apply(X))) + def FWG_op(X): + return PSF_apply(inverse(X)) + #Inverse operator + def IWG_op(X): + return transform(PSFT_apply(X)) #Forward Source operator def FS_op(X): @@ -373,164 +451,611 @@ def IS_op(X): return Finv_apply(PSFT_apply(X)) #Forward Lens operator def FG_op(X): - return (PSF_apply(X)) + return X#(PSF_apply(X)) #Inverse Lens operator def IG_op(X): - return (PSFT_apply(X)) + return X#(PSFT_apply(X)) + #Regularisation (Backward term) def regG0(X): return tools.Hard_Threshold(X, transform, inverse, levelg*kG) def regS0(X): return tools.Hard_Threshold(X, transform, inverse, levels*kS) def regG1(X): - return tools.Soft(X, levelg*weightG, k, supp=supp, Kill = Killg) + return tools.Soft(X, levelg*weightG, k, supp=1, Kill = Killg) def regS1(X): - return tools.Soft(X, levels*weightS, k, supp=supp, Kill = Kills) + return tools.Soft(X, levels*weightS, k , supp=supp, Kill = Kills) + def reg_plus(X): + X[X<0] = 0 + return X def reg_filter(X): return tools.mr_filter(X,levels,kmax,20,transform, inverse, I_op(sigma0*np.ones((n1,n2))), lvl = lvl, supp = supp) # Noise levels in image plane in starlet space levelg = tools.level(n1, n2, lvlg) * sigma0 + #Noise simulations to estimate noise levels in source plane - if np.sum(levels)==0: + if not np.any(levels): print('Calculating noise levels') levels = level_source(n1, n2, sigma0, size, PSFconj, Lens_op2, lensed, lvls) #levels[:,lensed ==0] = np.max(levels*10) #Saves levels hdus = pf.PrimaryHDU(levels) lists = pf.HDUList([hdus]) - lists.writeto('Noise_levels_MCA.fits', clobber=True) - + lists.writeto(noise_levels_file, clobber=True) - #Computationt of spectral norms FS_norm = spectralNorm(ns1,ns2,20,1e-10,FS_op,IS_op) - Star_norm_im = spectralNorm(n1,n2,20,1e-10,transform,inverse) - Star_norm_s = spectralNorm(ns1,ns2,20,1e-10,transform,inverse) - muG = 1./(2*Star_norm_im)**2 - muS = 1./(2*Star_norm_s*FS_norm)**2 - print(muS, muG) + FG_norm = spectralNorm(ns1, ns2, 20, 1e-10, FG_op, IG_op) + wave_norm_im = spectralNorm(n1,n2,20,1e-10,transform,inverse) + wave_norm_s = spectralNorm(ns1,ns2,20,1e-10,transform,inverse) + opwaveS_norm = spectralNorm(n1, n2, 20, 1e-10, IWS_op, FWS_op) + opwaveG_norm = spectralNorm(n1, n2, 20, 1e-10, IWG_op, FWG_op) + + + if scheme == 'Vu': + mu = 1. + tauG = 0.5/(mu*wave_norm_im**2+0.5*FG_norm) + tauS = 0.5 / (mu * wave_norm_s ** 2 + 0.5 * FS_norm) + if verbosity == 1: + print(tauS, tauG) + else: + muG = 1. / (opwaveG_norm) + muS = 1. / (opwaveS_norm) + if verbosity == 1: + print(muS, muG) weightS = WS weightG = WG + niter0 = np.copy(niter) + riter0 = np.copy(riter) #Reweighting loop - for it in range(3): + # k = tools.MOM(transform(Y), transform(Y), levelg, levelg) # ORIGINAL CODE + k = tools.MOM(transform(Y), transform(Y), levels, levelg) + k0 = np.copy(k) + karg = np.log(kmax / k0) / (niter - 10.) + + + if np.sum(Ginit) == 0: + G = np.random.randn(n1, n2) * sigma0 + else: + G = Ginit + if np.sum(Sinit) == 0: + S = np.random.randn(ns1, ns2) * sigma0 + else: + S = Sinit + + # FS = FG_op(G) # ORIGINAL CODE + # FG = FS_op(S) # ORIGINAL CODE + FS = 0 + FG = 0 + Gnew = np.copy(G) + Snew = np.copy(S) + alphaSnew = transform(S) + csiS = np.copy(alphaSnew) + alphaGnew = transform(G) + csiG = np.copy(alphaGnew) + + for it in range(nweight): #Initialisations + if it 5: + pointS = Criteria(j, Res1S, Res2S) + if pointS >= 5: + if verbosity == 1: + print('Convergence on S in:', j, ' iterations.') + break + if scheme == 'FISTA': + Snew = inverse(alphaSnew) + Snew[Snew<0] = 0 + FS = FS_op(Snew) + + DG = Y - FS - DG = Y-FS tg = 1 pointG = 0 Res1G = [] Res2G = [] - for j2 in range(riter): - G = np.copy(Gnew) - # G, M = tools.Forward_Backward(DG, G, FG_op, IG_op, muG, reg_filter, pos=1) - alphaG, csiG, tg = tools.FISTA(DG, alphaG, FG_op, IG_op, muG, tg, csiG, regG1, transform, inverse, pos = 1) - Gnew = inverse(alphaG) - FG = FG_op(Gnew) - Res1S.append(tools.Res(S,Snew,sigma0)) - Res2S.append(tools.SDR(S,Snew)) - pointS = Criteria(j,Res1S,Res2S, pointS) - # - - - Res1 = tootls.Res(Y, FS+FG, sigma0) - Res2 = (tools.SDR(Gnew, G)+tools.SDR(Snew, S))/2. - K_s[i] = np.mean(newres) - res = np.copy(newres) + + G = np.copy(Gnew) + pointG = 0 + for j2 in range(1): + if scheme == 'FISTA': + alphaG = np.copy(alphaGnew) + alphaGnew, csiG, tg = tools.FISTA(DG, alphaG, FG_op, IG_op, muG, tg, csiG, regG1, transform, inverse, pos = 0) + + + + if scheme == 'Vu': + alphaG = np.copy(alphaGnew) + G = np.copy(Gnew) + Gnew, alphaGnew = tools.Vu_Primal_dual(DG, G, alphaG, mu, tauG, FG_op, IG_op, transform, inverse, regG1, + reg_plus) + Res2G.append(tools.SDR(alphaG, alphaGnew)) + + if j2>5: + pointG = Criteria(j2, Res1G, Res2G) + if pointG >=5: + if verbosity == 1: + print('Convergence on S in:', j2, ' iterations.') + break + if scheme == 'FISTA': + Gnew = inverse(alphaGnew) + Gnew[Gnew<0] = 0 + FG = FG_op(Gnew) + + + + + Res1.append(tools.Res(Y, FS+FG, sigma0)) + Res2.append((tools.SDR(Gnew, G)+tools.SDR(Snew, S))/2.) + + if i>5: - points = Criteria(i,Res1, Res2, points) - if points >= 10: - print('BREAK: algorithm converged at iteration: ', i) + points = Criteria(i, Res2, Res1) + if points >= 5: + if verbosity ==1: + print('BREAK: algorithm converged at iteration: ', i) break - - plt.figure(0) - plt.subplot(221) - plt.title('S') - plt.imshow(Snew) - plt.subplot(222) - plt.title('FS') - plt.imshow(FS) - plt.subplot(223) - plt.title('FG') - plt.imshow(FG) - plt.subplot(224) - plt.title('Residuals') - plt.imshow(Y-FS-FG) - plt.savefig('Res'+str(i)+'.png') + if verbosity ==1: + plt.figure(0) + plt.subplot(221) + plt.title('S') + plt.imshow(Snew, origin='lower') + plt.subplot(222) + plt.title('FS') + plt.imshow(FS, origin='lower') + plt.subplot(223) + plt.title('FG') + plt.imshow(FG, origin='lower') + plt.subplot(224) + plt.title('Residuals') + plt.imshow(Y-FS-FG, origin='lower') + plt.savefig('Res'+str(i)+'.png') i +=1 #Weighting - - weightS = 1./(1.+np.exp(-10.*(levels*kmax-alphaS))) - weightG = 1./(1.+np.exp(-10.*(levelg*kmax-alphaG))) + + weightS = 2./(1.+np.exp(-10.*(levels*kmax-alphaSnew))) + weightG = 2./(1.+np.exp(-10.*(levelg*kmax-alphaGnew))) - # S, FS = SLIT(Y-G, Fkappa, kmax, niter, size, PSF, PSFconj, levels = [0], scheme = 'FISTA', mask = mask, lvl = lvls) + # Snew, FS = SLIT(Y-FG, Fkappa, kmax, niter, size, PSF, PSFconj, levels = [0], scheme = 'FISTA', mask = mask, lvl = lvls) #Final reconstructions - plt.show() - plt.figure(1) - plt.subplot(211) - plt.plot(Res1) - plt.subplot(212) - plt.plot(Res2) - plt.show() - return Snew, FS,Gnew, FG + if verbosity == 2: + plt.figure(1) + plt.subplot(211) + plt.plot(Res1) + plt.subplot(212) + plt.plot(Res2) + plt.show() + return Snew, FS,Gnew, FG, Res1, Res2 +def SLIT_MCA_HR(Y, Fkappa, kmax, niter, riter, size, PSF, lvlg=0, lvls=0, noise='gaussian', scheme='FISTA', + tau=0, levels=[0], WS=1, WG=1, mask=[0, 0], Ginit=0, Kills=0, Killg=0, verbosity=0, nweight=5): + ##DESCRIPTION: + ## Function that estimates the source and lens light profiles from an image of a + ## strong lens system + ## + ##INPUTS: + ## -img: a 2-D image of a lensed source given as n1xn2 numpy array. + ## -Fkappa: an array giving the mapping between lens and source. This array is calculated from the lens mass density + ## using tools from SLIT.Lens + ## -kmax: the detection threshold in units of noise levels. We usualy set this value to 5 to get a 5 sigma + ## detection threshold. + ## -niter: maximal number of iterations in the main loop over G. + ## -riter: maximal number of iterations in the inner loop over S. + ## -size: resoluution factor between lens and source grids such thathe size of the output source + ## will be n1sizexn2size + ## -PSF: the point spread function of the observation provided as a 2D array. + ## -PSFconj: The conjugate of the PSF. Usually computed via np.real(np.fft.ifft2(np.conjugate(np.fft.fft2(PSF0[:-1,:-1])))) + ## butthe user has to make sure that the conjugate is well centered. + ## + ##OPTIONS: + ## -levels: an array that contains the noise levels at each band of the wavelet decomposition of the source. + ## If not provided, the routine will compute the levels and save them in a fits file 'Noise_levels.fits' + ## so that they can be used at a later time. This option allows to save time when running the same + ## experiment several times. + ## -mask: an array of zeros and one with size ns1xns2. The zeros will stand for masked data. + ## -Ginit: Educated guedd for the lens galaxy light profile. if set to a 2D numpy array, the array will be used as + ## as an initialisation for G. + ## + ##OUTPUTS: + ## -S: the source light profile. + ## -G: the convolved lens light profile + ## -FS: the lensed version of the estimated source light profile + ## + ##EXAMPLE: + ## S,FS = SLIT(img, Fkappa, 5, 100, 1, PSF, PSFconj) + + niter = max([6, niter]) + + # Shape of the image + n1, n2 = np.shape(Y) + # Initialisation of the source + ns1 = n1 * size + ns2 = n2 * size + PSFconj = PSF.T + # Number of starlet scales in source and image planes + if lvlg == 0: + lvlg = np.int(np.log2(n2)) + else: + lvlg = np.min([lvlg, np.int(np.log2(n2))]) + lvls = lvlg + if lvls > np.int(np.log2(ns2)): + print('Error, too many wavelet levels for the source. Choose a smaller value for lvl') + exit + # Masking if required + if np.sum(mask) == 0: + mask = np.ones((n1, n2)) + Y = Y * mask + # Noise standard deviation in image plane + if noise == 'gaussian': + print('noise statistic is gaussian') + sigma0 = tools.MAD(Y) + if noise == 'poisson': + print('noise statistic is poisson') + sigma0 = tools.MAD_poisson(Y, tau) + if (noise == 'G+P') or (noise == 'P+G'): + print('noise statistic is poisson and gaussian mixture') + sigma0 = np.sqrt(tools.MAD_poisson(Y, tau, lvlg) ** 2 + tools.MAD(Y) ** 2) + + # Mapping of an all-at-one image + lensed = lens_one(Fkappa, ns1, ns2, 1) + + supp = np.zeros((lvls, lensed.shape[0], lensed.shape[1])) + supp[:, lensed / lensed == 1] = 1 + + # Limits of the image plane in source plane + bound = mk_bound(Fkappa, ns1, ns2, 1) + + # Useful functions + def Down(I): + return tools.Downsample(I, size) + + def Up(I): + return tools.Upsample(I, size) + + def Finv_apply(I): + return Lens.image_to_source(I, 1, Fkappa, lensed=lensed) + + def Lens_op2(I): + return Lens.image_to_source(I, 1, Fkappa, lensed=lensed, square=1) + + def F_apply(Si): + return Lens.source_to_image(Si, ns1, ns2, Fkappa) + + def PSF_apply(i): + return scp.fftconvolve(i, PSF, mode='same') + + def PSFT_apply(ii): + return scp.fftconvolve(ii, PSFconj, mode='same') + + def transform(x): + coeffs, _ = tools.wave_transform(x, lvlg, newwave=1) + return coeffs + + def inverse(x): + return tools.iuwt(x, newwave=1) + + def FWS_op(X): + return Down(PSF_apply(F_apply(inverse(X)))) + + # Inverse operator + def IWS_op(X): + return transform(Finv_apply(PSFT_apply(Up(X)))) + + def FWG_op(X): + return inverse(X) + + # Inverse operator + def IWG_op(X): + return transform(X) + + # Forward Source operator + def FS_op(X): + return Down(PSF_apply(F_apply(X))) + + # Inverse Source operator + def IS_op(X): + return Finv_apply(PSFT_apply(Up(X))) + + # Forward Lens operator + def FG_op(X): + return X # (PSF_apply(X)) + + # Inverse Lens operator + def IG_op(X): + return X # (PSFT_apply(X)) + + # Regularisation (Backward term) + def regG0(X): + return tools.Hard_Threshold(X, transform, inverse, levelg * kG) + + def regS0(X): + return tools.Hard_Threshold(X, transform, inverse, levels * kS) + + def regG1(X): + return tools.Soft(X, levelg * weightG, k, supp=1, Kill=Killg) + + def regS1(X): + return tools.Soft(X, levels * weightS, k, supp=supp, Kill=Kills) + + def reg_plus(X): + X[X < 0] = 0 + return X + + def reg_filter(X): + return tools.mr_filter(X, levels, kmax, 20, transform, inverse, I_op(sigma0 * np.ones((n1, n2))), lvl=lvl, + supp=supp) + + # Noise levels in image plane in starlet space + levelg = tools.level(n1, n2, lvlg) * sigma0 + # Noise simulations to estimate noise levels in source plane + if np.sum(levels) == 0: + print('Calculating noise levels') + levels = level_source_HR(n1, n2, size, sigma0, PSFconj, Lens_op2, Up, lvls) + # levels[:,lensed ==0] = np.max(levels*10) + # Saves levels + hdus = pf.PrimaryHDU(levels) + lists = pf.HDUList([hdus]) + lists.writeto('Noise_levels_MCA.fits', clobber=True) + + # Computationt of spectral norms + FS_norm = spectralNorm(ns1, ns2, 20, 1e-10, FS_op, IS_op) + FG_norm = spectralNorm(ns1, ns2, 20, 1e-10, FG_op, IG_op) + wave_norm_im = spectralNorm(ns1, ns2, 20, 1e-10, transform, inverse) + wave_norm_s = spectralNorm(ns1, ns2, 20, 1e-10, transform, inverse) + opwaveS_norm = spectralNorm(n1, n2, 20, 1e-10, IWS_op, FWS_op) + opwaveG_norm = spectralNorm(n1, n2, 20, 1e-10, IWG_op, FWG_op) + + if scheme == 'Vu': + mu = 1. + tauG = 0.5 / (mu * wave_norm_im ** 2 + 0.5 * FG_norm) + tauS = 0.5 / (mu * wave_norm_s ** 2 + 0.5 * FS_norm) + if verbosity == 1: + print(tauS, tauG) + + else: + muG = 1. / (opwaveG_norm) + muS = 1. / (opwaveS_norm) + if verbosity == 1: + print(muS, muG) + weightS = WS + weightG = WG + + niter0 = np.copy(niter) + riter0 = np.copy(riter) + # Reweighting loop + + for it in range(nweight): + # Initialisations + + if it < np.max(range(nweight)): + niter = niter0 # /2 + riter = riter0 # /2 + else: + niter = niter0 + riter = riter0 + + i = 0 + tg = 1 + ts = 1 + + FS = 0 + FG = 0 + G = np.random.randn(n1, n2) * sigma0 + S = np.random.randn(ns1, ns2) * sigma0 + Gnew = np.copy(G) + Snew = np.copy(S) + alphaSnew = transform(S) + csiS = np.copy(alphaSnew) + alphaGnew = transform(G) + csiG = np.copy(alphaGnew) + + k = tools.MOM(transform(Y), transform(Y), levels, levelg) / 100. + k0 = np.copy(k) + karg = np.log(kmax / k0) / (niter - 5.) + print(k) + step = (k - kmax) / (niter - 5) + Res1 = [] + Res2 = [] + DS = np.copy(Y) + DG = np.copy(Y) + + # Beginning of main loop + points = 0 + Res1G = [1, 2] + Res1S = [1, 2] + while i < niter: + + k = k0 * np.exp(i * karg) + kMOM = tools.MOM(transform(DS), transform(DG), levels, levelg) + + if kMOM < k: + k = np.copy(kMOM) + print('MOMs threshold: ', k) + step = (k - kmax) / (niter - i - 5) + + k = np.max([kmax, k]) + print('main loop: ', i, k, kMOM) + + DG = Y - FS + + tg = 1 + pointG = 0 + Res1G = [] + Res2G = [] + G = np.copy(Gnew) + pointG = 0 + for j2 in range(1): + if scheme == 'FISTA': + alphaG = np.copy(alphaGnew) + alphaGnew, csiG, tg = tools.FISTA(DG, alphaG, FG_op, IG_op, muG, tg, csiG, regG1, transform, + inverse, pos=0) + + if scheme == 'Vu': + alphaG = np.copy(alphaGnew) + G = np.copy(Gnew) + Gnew, alphaGnew = tools.Vu_Primal_dual(DG, G, alphaG, mu, tauG, FG_op, IG_op, transform, inverse, + regG1, + reg_plus) + Res2G.append(tools.SDR(alphaG, alphaGnew)) + + if j2 > 5: + pointG = Criteria(j2, Res1G, Res2G) + if pointG >= 5: + if verbosity == 1: + print('Convergence on S in:', j2, ' iterations.') + break + if scheme == 'FISTA': + Gnew = inverse(alphaGnew) + Gnew[Gnew < 0] = 0 + FG = FG_op(Gnew) + + DS = Y - FG + + ts = 1 + pointS = 0 + Res1S = [] + Res2S = [] + pointS = 0 + for j in range(riter): + if scheme == 'FISTA': + alphaS = np.copy(alphaSnew) + alphaSnew, csiS, ts = tools.FISTA(DS, alphaS, FS_op, IS_op, muS, ts, csiS, regS1, transform, + inverse, pos=0) + + if scheme == 'Vu': + alphaS = np.copy(alphaSnew) + S = np.copy(Snew) + Snew, alphaSnew = tools.Vu_Primal_dual(DS, S, alphaS, mu, tauS, FS_op, IS_op, transform, inverse, + regS1, reg_plus) + Res2S.append(tools.SDR(alphaS, alphaSnew)) + + if j > 5: + pointS = Criteria(j, Res1S, Res2S) + if pointS >= 5: + if verbosity == 1: + print('Convergence on S in:', j, ' iterations.') + break + if scheme == 'FISTA': + Snew = inverse(alphaSnew) + Snew[Snew < 0] = 0 + FS = FS_op(Snew) + + Res1.append(tools.Res(Y, FS + FG, sigma0)) + Res2.append((tools.SDR(Gnew, G) + tools.SDR(Snew, S)) / 2.) + + if i > 5: + points = Criteria(i, Res2, Res1) + if points >= 5: + if verbosity == 1: + print('BREAK: algorithm converged at iteration: ', i) + break + if verbosity == 1: + plt.figure(0) + plt.subplot(221) + plt.title('S') + plt.imshow(Snew, origin='lower') + plt.subplot(222) + plt.title('FS') + plt.imshow(FS, origin='lower') + plt.subplot(223) + plt.title('FG') + plt.imshow(FG, origin='lower') + plt.subplot(224) + plt.title('Residuals') + plt.imshow(Y - FS - FG, origin='lower') + plt.savefig('Res' + str(i) + '.png') + i += 1 + # Weighting + + weightS = 2. / (1. + np.exp(-10. * (levels * kmax - alphaSnew))) + weightG = 2. / (1. + np.exp(-10. * (levelg * kmax - alphaGnew))) + + # Snew, FS = SLIT(Y-FG, Fkappa, kmax, niter, size, PSF, PSFconj, levels = [0], scheme = 'FISTA', mask = mask, lvl = lvls) + + # Final reconstructions + if verbosity == 2: + plt.show() + plt.figure(1) + plt.subplot(211) + plt.plot(Res1) + plt.subplot(212) + plt.plot(Res2) + plt.show() + return Snew, FS, Gnew, FG ################################### TOOLS ################################### @@ -539,10 +1064,14 @@ def Criteria(i, Res1, Res2): # if np.abs(Res1[-1]-1) < 0.01: # point_res += 1 - if (np.abs(Res2[-1] - Res2[-2]) < 0.01*np.abs(Res2[0]-Res2[1])) and (np.abs(Res1[-1] - Res1[-2]) < 0.001*np.abs(Res1[0]-Res1[1])): + + if (np.abs(Res2[-1] - Res2[-2]) < 0.1) and Res2[-1]<2.:#*np.abs(Res2[0]-Res2[1])):# and (np.abs(Res1[-1] - Res1[-2]) < 0.01*np.abs(Res1[0]-Res1[1])): points = 1 else: points = 0 + if np.size(Res1)>5: + if (np.abs(Res1[-1] - Res1[-2]) < 0.1*np.abs(Res1[1]-Res1[0])) and Res1[-1]>10.: + points+=1 return points @@ -563,24 +1092,55 @@ def plot_cube(cube): j = 2 for k in range(n): plt.subplot(i,j,k) - plt.imshow(cube[k,:,:]); plt.colorbar() + plt.imshow(cube[k,:,:], origin='lower'); plt.colorbar() return None +def level_source_HR(n1,n2, size, sigma,PSFT, Lens_op2, Up, lvl): + ns1,ns2 = int(n1*size), int(n2*size) + ones = np.ones((n1,n2)) + noise = Up(ones*sigma)*(size)**2 + Hnoise = np.sqrt(scp.fftconvolve(noise**2, PSFT**2, mode = 'same'))#noise*np.sqrt(np.sum(PSFT**2))## + Hnoise[np.isnan(Hnoise)==1] = 0 + FHnoise_old = Lens_op2(Hnoise) + FHnoise = np.copy(FHnoise_old) + FHnoise[FHnoise_old==0] = np.mean(FHnoise_old)*10. + dirac = np.zeros((ns1,ns2)) + dirac[int(ns1/2),int(ns2/2)] = 1 + print(dirac.shape, ns1,ns2) + wave_dirac, _ = tools.wave_transform(dirac, lvl) + levels = np.zeros(wave_dirac.shape) + for i in range(lvl): + if np.size(noise.shape) > 2: + lvlso = (scp.fftconvolve(FHnoise[i, :, :] ** 2, wave_dirac[i, :, :] ** 2, + mode='same')) + else: + lvlso = scp.fftconvolve(FHnoise ** 2, wave_dirac[i,:,:] ** 2, + mode='same') + #lvlso[lensed == 0] = np.max(lvlso)*100000000 + levels[i, :, :] = np.sqrt(np.abs(lvlso)) + levels[i,lvlso == 0] = 0 + return levels + + def level_source(n1,n2,sigma,size,PSFT, Lens_op2, lensed, lvl): - ns1,ns2 = n1*size, n2*size + ns1,ns2 = int(n1*size), int(n2*size) ones = np.ones((n1,n2)) lensed[lensed == 0] = 1 noise = ones*sigma - Hnoise = np.sqrt(scp.fftconvolve(noise**2, PSFT**2, mode = 'same'))#noise*np.sqrt(np.sum(PSFT**2))## + + Hnoise = noise*np.sqrt(np.sum(PSFT**2))##np.sqrt(scp.fftconvolve(noise**2, PSFT**2, mode = 'same'))#noise*np.sqrt(np.sum(PSFT**2))## + Hnoise[np.isnan(Hnoise)==1] = 0 FHnoise_old = Lens_op2(Hnoise) FHnoise = np.copy(FHnoise_old) FHnoise[FHnoise_old==0] = np.mean(FHnoise_old)*10. dirac = np.zeros((ns1,ns2)) - dirac[ns1/2,ns2/2] = 1 - wave_dirac = tools.wave_transform(dirac, lvl) + + dirac[int(ns1/2),int(ns2/2)] = 1 + + wave_dirac, _ = tools.wave_transform(dirac, lvl) levels = np.zeros(wave_dirac.shape) for i in range(lvl): if np.size(noise.shape) > 2: @@ -596,11 +1156,10 @@ def level_source(n1,n2,sigma,size,PSFT, Lens_op2, lensed, lvl): def spectralNorm(n1,n2,Niter,tol,f,finv): ##DESCRIPTION: - ## Function that estimates the source light profile from an image of a lensed source given the mass density profile. + ## Function that computes the spectral norm of an operator f ## ##INPUTS: - ## -nx,ny: shape of the input - ## -nz: number of decomposition scales (if the operator tis a multiscale decomposition for instance) + ## -n1,n2: shape of the input ## -Niter: number of iterations ## -tol: tolerance error as a stopping criteria ## -f: operator @@ -659,7 +1218,9 @@ def mk_bound(Fkappa, n1,n2,size): ##OUTPUTS: ## -lensed: the projection to source plane of an all at aone image. dirac = np.ones((n1,n2)) - lensed = Lens.image_to_source_bound(dirac, size,Fkappa,lensed = [0]) + + lensed = Lens.image_to_source_bound(dirac, size, Fkappa,lensed = [0]) + bound = lensed/lensed bound[lensed==0]=0 return bound @@ -667,7 +1228,7 @@ def mk_bound(Fkappa, n1,n2,size): def mk_simu(n1,n2,lvl,size, sigma, I_op, transform, n): - storage = np.zeros((lvl,n1*size, n2*size, n)) + storage = np.zeros((lvl, int(n1*size), int(n2*size), n)) for i in range(n): noise = np.random.randn(n1,n2)*sigma noise_lens = I_op(noise) @@ -693,10 +1254,12 @@ def simulate_noise(n1,n2, sigma, size, I_op, transform, lvl, Npar = np.int(mtp.c ##OUTPUTS: ## -S: the source light profile. ## -FS: the lensed version of the estimated source light profile + from pathos.multiprocessing import ProcessingPool as Pool + n = 500 if Npar>mtp.cpu_count(): Npar = mtp.cpu_count() - ns1,ns2 = n1*size, n2*size + ns1,ns2 = int(n1*size), int(n2*size) # lvl = np.int(np.log2(ns1)) w_levels = np.zeros((lvl,ns1,ns2)) diff --git a/SLIT/Solve.pyc b/SLIT/Solve.pyc deleted file mode 100644 index f203a8d..0000000 Binary files a/SLIT/Solve.pyc and /dev/null differ diff --git a/SLIT/__init__.py b/SLIT/__init__.py index a7d6663..e69de29 100755 --- a/SLIT/__init__.py +++ b/SLIT/__init__.py @@ -1,4 +0,0 @@ -from Solve import * -import Lens -import wave_transform -import tools diff --git a/SLIT/__init__.pyc b/SLIT/__init__.pyc deleted file mode 100755 index 0fcdf27..0000000 Binary files a/SLIT/__init__.pyc and /dev/null differ diff --git a/SLIT/gaussian.py b/SLIT/gaussian.py new file mode 100644 index 0000000..eefe625 --- /dev/null +++ b/SLIT/gaussian.py @@ -0,0 +1,176 @@ +import numpy as np +import scipy.misc as spm +import matplotlib.pyplot as plt +import matplotlib.cm as cm + + +def gaussian(n1,n2,x0,y0,A,e1,e2,alpha): + #img = gaussian(n1,n2,x0,y0,A,e1,e2,alpha) + #produces a gaussian profile image + #INPUTS: + # n1,n2: size of the output image + # x0,y0: centroid of the gaussian profile + # A: value of the maximum value for the gaussian profile + # e1,e2: ellipticity og the profile + # alpha: inclination of the profile + #OUTPUTS: + # img: n1xn2 image containing the gaussian profile + + Img = np.zeros([n1,n2]) + valcor = np.zeros([2,n1*n2]) + + AA = np.zeros([n1,n2]) + + xx0 = np.zeros(n1*n2) + xx0[:]=x0 + yy0 = np.zeros(n2*n1) + yy0[:]=y0 + coord0 = np.zeros([2, n1*n2]) + coord = np.zeros([2, n1*n2]) + + # terme d'amplitude + ampli = A/(2*np.pi*np.sqrt(e1*e2)) + + mat_rot = [[np.cos(alpha), np.sin(alpha)],[-np.sin(alpha), np.cos(alpha)]] + tmat_rot = np.transpose(mat_rot) + matell = [[(e1*e1),0],[0,(e2*e2)]] + + # Matrice des moments quadripolaires + matA = np.mat(np.dot(np.dot(tmat_rot,matell),mat_rot)) + + xc, yc = np.where(Img == 0) + ii = np.array(xc) + jj = np.array(yc) + #print(np.shape(i), np.shape(xx0)) + count = np.linspace(0,n1*n2-1, n1*n2-1, dtype=int) + + valcor = np.array([ii,jj]) - np.array([xx0,yy0]) + valcor = np.array(valcor) + for k in count: + val = np.mat(valcor[:,k]) + invA = np.array(np.linalg.inv(matA)) + var = np.dot(np.dot(val,invA),np.transpose(val)) + AA[ii[k],jj[k]]= var + + + Img = (ampli*np.exp(-0.5*AA)) + + return Img + +def moffat(n1,n2,x0,y0,A,e1,e2,alpha,beta): + #img = gaussian(n1,n2,x0,y0,A,e1,e2,alpha) + #produces a gaussian profile image + #INPUTS: + # n1,n2: size of the output image + # x0,y0: centroid of the gaussian profile + # A: value of the maximum value for the gaussian profile + # e1,e2: ellipticity og the profile + # alpha: inclination of the profile + #OUTPUTS: + # img: n1xn2 image containing the gaussian profile + + Img = np.zeros([n1,n2]) + valcor = np.zeros([2,n1*n2]) + + AA = np.zeros([n1,n2]) + + xx0 = np.zeros(n1*n2) + xx0[:]=x0 + yy0 = np.zeros(n2*n1) + yy0[:]=y0 + coord0 = np.zeros([2, n1*n2]) + coord = np.zeros([2, n1*n2]) + + # terme d'amplitude + ampli = A/(2*np.pi*np.sqrt(e1*e2)) + + mat_rot = [[np.cos(alpha), np.sin(alpha)],[-np.sin(alpha), np.cos(alpha)]] + tmat_rot = np.transpose(mat_rot) + matell = [[1./(e1*e1),0],[0,1./(e2*e2)]] + + # Matrice des moments quadripolaires + matA = np.mat(np.dot(np.dot(tmat_rot,matell),mat_rot)) + + xc, yc = np.where(Img == 0) + i = np.array(xc) + j = np.array(yc) + #print(np.shape(i), np.shape(xx0)) + count = np.linspace(0,n1*n2-1, n1*n2-1, dtype=int) + + valcor = np.array([i,j]) - np.array([xx0,yy0]) + valcor = np.array(valcor) + for k in count: + val = np.mat(valcor[:,k]) + invA = np.array(np.linalg.inv(matA)) + var = np.dot(np.dot(val,invA),np.transpose(val)) + AA[i[k],j[k]]= var + + + Img = (ampli*(1+AA**2)**(-beta)) + + return Img + +def sersic(n1,n2,x0,y0,A,e1,e2,alpha,n): + #img = gaussian(n1,n2,x0,y0,A,e1,e2,alpha) + #produces a gaussian profile image + #INPUTS: + # n1,n2: size of the output image + # x0,y0: centroid of the gaussian profile + # A: value of the maximum value for the gaussian profile + # e1,e2: ellipticity og the profile + # alpha: inclination of the profile + #OUTPUTS: + # img: n1xn2 image containing the gaussian profile + + Img = np.zeros([n1,n2]) + valcor = np.zeros([2,n1*n2]) + + AA = np.zeros([n1,n2]) + + xx0 = np.zeros(n1*n2) + xx0[:]=x0 + yy0 = np.zeros(n2*n1) + yy0[:]=y0 + coord0 = np.zeros([2, n1*n2]) + coord = np.zeros([2, n1*n2]) + + # terme d'amplitude + ampli = A/(2*np.pi*np.sqrt(e1*e2)) + + mat_rot = [[np.cos(alpha), np.sin(alpha)],[-np.sin(alpha), np.cos(alpha)]] + tmat_rot = np.transpose(mat_rot) + matell = [[1./(e1*e1),0],[0,1./(e2*e2)]] + + # Matrice des moments quadripolaires + matA = np.mat(np.dot(np.dot(tmat_rot,matell),mat_rot)) + + xc, yc = np.where(Img == 0) + i = np.array(xc) + j = np.array(yc) + #print(np.shape(i), np.shape(xx0)) + count = np.linspace(0,n1*n2-1, n1*n2-1) + count = np.int_(count) + + valcor = np.array([i,j]) - np.array([xx0,yy0]) + valcor = np.array(valcor) + for k in count: + val = np.mat(valcor[:,k]) + invA = np.array(np.linalg.inv(matA)) + var = np.dot(np.dot(val,invA),np.transpose(val)) + AA[i[k],j[k]]= var + + + Img = (ampli*np.exp(-AA**(1/n))) + + return Img + + +def add_noise(img, mean, sigma): + shp = np.shape(img) + n1 = shp[0] + cov = numpy.identity(2) + noise = np.random.multovariate_normal([mean,mean], cov, [128,128] ) + imfinal = img+noise[:,:,0] + return imfinal + + diff --git a/SLIT/mk_SLIT_plot.py b/SLIT/mk_SLIT_plot.py new file mode 100644 index 0000000..09881cd --- /dev/null +++ b/SLIT/mk_SLIT_plot.py @@ -0,0 +1,374 @@ +import matplotlib.cm as cm +import matplotlib.pyplot as plt +import numpy as np +from SLIT import Lens +import scipy.signal as scp +import scipy.misc as misc + +def plot_critical(kappa, Fkappa, n1,n2, size, extra= 1): + + det = 1./Lens.Jacobian_det(kappa, n1,n2)[extra/2:-extra/2., extra/2:-extra/2.] + + + kernel = np.array([[1,0],[0,-1]]) + kernelT = np.array([[0,1],[-1,0]]) + diff = np.abs(-det+np.abs(det)) + + diff[diff!=0]=1 + xderiv = scp.convolve2d(diff, kernel, mode='same') + yderiv = scp.convolve2d(diff, kernelT, mode='same') + + + + x,y = np.where(np.abs(xderiv)+np.abs(yderiv)>0) + #newx,newy = mk_curve(x,y) + critical = np.zeros((n1,n2)) + critical[x,y] = 1 + + Splane = Lens.image_to_source(critical, Fkappa, 0) + + xs,ys = np.where(Splane !=0) + #newxs,newys = mk_curve(xs,ys) + factor = np.float(size) + return x/factor,y/factor, xs, ys + +def mk_curve(x,y): + + newx, newy = np.zeros(np.size(x)+1), np.zeros(np.size(y)+1) + newx[0], newy[0] = x[0], y[0] + newx[-1], newy[-1] = x[0], y[0] + x[0],y[0] = -999,-999 + for i in range(x.size-1): + + + r = (newx[i]-x)**2+(newy[i]-y)**2 + + + if np.size(np.where(r == np.min(r)))>1: + newx[i + 1], newy[i + 1] = int(x[(r == np.min(r)) * (r != 0)][0]), int(y[(r == np.min(r)) * (r != 0)][0]) + + else: + newx[i+1], newy[i+1] = int(x[(r == np.min(r))*(r!=0)]), int(y[(r == np.min(r))*(r!=0)]) + x[(newx[i+1]-x)**2+(newy[i+1]-y)**2==0], y[(newx[i+1]-x)**2+(newy[i+1]-y)**2==0] =-999,-999 + return (newy.astype(int)), (newx.astype(int)) + +def Plot_SLIT_Results(Y,S,FS, TrueS, TrueFS, sigma, TitleFont = 40, ColorbarFont = 25, x=[0], y=[0], xs = [0], ys = [0], delta_pix = 0): + ns1,ns2 = S.shape + n1,n2 = Y.shape + size = ns1 / np.float(n1) + if delta_pix > 0: + L = 1. / delta_pix # Length of 1 arceseconds in pixels + Ls = L * size + XXarc = [n1 / 10, n1 / 10 + L] + XYarc = [n2 / 10, n2 / 10] + YYarc = [n2 / 10, n2 / 10 + L] + YXarc = [n1 / 10, n1 / 10] + XXarcs = [ns1 / 10, ns1 / 10 + Ls] + XYarcs = [ns2 / 10, ns2 / 10] + YYarcs = [ns2 / 10, ns2 / 10 + Ls] + YXarcs = [ns1 / 10, ns1 / 10] + + plt.figure(0) + plt.title('$\~{S}$', fontsize=TitleFont) + plt.imshow((S), vmin=np.min(TrueS), vmax=np.max(TrueS), cmap=cm.gist_stern, interpolation='nearest') + plt.plot(ys, xs, 'w.', ms=2) + if delta_pix >0: + plt.plot(XXarc, XYarc, 'w', linewidth = 10 ) + plt.plot(YXarc, YYarc, 'w', linewidth = 10 ) + plt.text(n1/5+10, n2/5+10, '$1\"$', color = 'white', fontsize = 25 ) + plt.axis('off') + plt.xlim(xmax = ns1) + plt.ylim(ymax = ns2) + plt.xlim(xmin=0) + plt.ylim(ymin=0) + cbar = plt.colorbar() + cbar.ax.tick_params(labelsize=ColorbarFont) + plt.figure(1) + plt.title('$S$', fontsize=TitleFont) + plt.imshow(TrueS, cmap=cm.gist_stern, interpolation='nearest') + plt.plot(ys, xs, 'w.', ms=2) + plt.axis('off') + plt.xlim(xmax = ns1) + plt.ylim(ymax = ns2) + plt.xlim(xmin=0) + plt.ylim(ymin=0) + cbar = plt.colorbar() + cbar.ax.tick_params(labelsize=ColorbarFont) + plt.figure(2) + plt.title('$|S-\~S|$', fontsize=TitleFont) + diff = (TrueS - S) + plt.imshow((np.abs(diff)), cmap=cm.gist_stern, interpolation='nearest') + plt.plot(ys, xs, 'w.', ms=2) + plt.axis('off') + plt.xlim(xmax = ns1) + plt.ylim(ymax = ns2) + plt.xlim(xmin=0) + plt.ylim(ymin=0) + cbar = plt.colorbar() + cbar.ax.tick_params(labelsize=ColorbarFont) + ####Lensed source + plt.figure(3) + plt.title('$HFS$', fontsize=TitleFont) + plt.imshow(TrueFS, cmap=cm.gist_stern, interpolation='nearest') + plt.plot(y, x, 'w.', ms=2) + plt.axis('off') + plt.xlim(xmax = n1) + plt.ylim(ymax = n2) + plt.xlim(xmin=0) + plt.ylim(ymin=0) + cbar = plt.colorbar() + cbar.ax.tick_params(labelsize=ColorbarFont) + plt.figure(4) + plt.title('$HF\~S$', fontsize=TitleFont) + plt.imshow((FS), vmin=np.min(TrueFS), vmax=np.max(TrueFS), cmap=cm.gist_stern, interpolation='nearest') + plt.plot(y, x, 'w.', ms=2) + plt.axis('off') + plt.xlim(xmax = n1) + plt.ylim(ymax = n2) + plt.xlim(xmin=0) + plt.ylim(ymin=0) + cbar = plt.colorbar() + cbar.ax.tick_params(labelsize=ColorbarFont) + plt.figure(5) + plt.title('$|HFS-HF\~S|$', fontsize=TitleFont) + plt.imshow((TrueFS - FS), cmap=cm.gist_stern, interpolation='nearest') + plt.plot(y, x, 'w.', ms=2) + plt.axis('off') + plt.xlim(xmax = n1) + plt.ylim(ymax = n2) + plt.xlim(xmin=0) + plt.ylim(ymin=0) + cbar = plt.colorbar() + cbar.ax.tick_params(labelsize=ColorbarFont) + ###Image + plt.figure(8) + plt.title('$Y$', fontsize=TitleFont) + plt.imshow(Y, cmap=cm.gist_stern, interpolation='nearest') + plt.plot(y, x, 'w.', ms=2) + plt.axis('off') + plt.xlim(xmax = n1) + plt.ylim(ymax = n2) + plt.xlim(xmin=0) + plt.ylim(ymin=0) + cbar = plt.colorbar() + cbar.ax.tick_params(labelsize=ColorbarFont) + plt.figure(10) + plt.title('$|Y-HF\~S|$', fontsize=TitleFont) + plt.imshow(Y - FS, cmap=cm.gist_stern, interpolation='nearest', vmin=-5 * sigma, + vmax=5 * sigma) # slit.fft_convolve(Im,PSF) + plt.plot(y, x, 'w.', ms=2) + plt.axis('off') + plt.xlim(xmax = n1) + plt.ylim(ymax = n2) + plt.xlim(xmin=0) + plt.ylim(ymin=0) + cbar = plt.colorbar() + cbar.ax.tick_params(labelsize=ColorbarFont) + plt.show() + return 0 + +def Plot_MCA_Results(Y,S,FS,G,FG, TrueS, TrueG, TrueFS, sigma, TitleFont = 40, ColorbarFont = 25, x=[0], y=[0], xs = [0], ys = [0], delta_pix = 0): + + ns1,ns2 = S.shape + n1,n2 = G.shape + size = ns1/np.float(n1) + if delta_pix > 0: + L = 1. / delta_pix # Length of 1 arceseconds in pixels + Ls = L*size + XXarc = [n1 / 10, n1 / 10 + L] + XYarc = [n2 / 10, n2 / 10] + YYarc = [n2 / 10, n2 / 10 + L] + YXarc = [n1 / 10, n1 / 10] + XXarcs = [ns1 / 10, ns1 / 10 + Ls] + XYarcs = [ns2 / 10, ns2 / 10] + YYarcs = [ns2 / 10, ns2 / 10 + Ls] + YXarcs = [ns1 / 10, ns1 / 10] + + plt.figure(0) + plt.title('$\~{S}$', fontsize=TitleFont) + plt.imshow((S), vmin=np.min(TrueS), vmax=np.max(TrueS), cmap=cm.gist_stern, interpolation='nearest') + plt.plot(ys,xs,'w.', ms = 2) + plt.axis('off') + plt.xlim(xmax=ns1) + plt.ylim(ymax=ns2) + plt.xlim(xmin=0) + plt.ylim(ymin=0) + if delta_pix > 0: + plt.plot(XXarcs, XYarcs, 'w', linewidth=3) + plt.plot(YXarcs, YYarcs, 'w', linewidth=3) + plt.text(ns1 / 10 + 5, ns2 / 10 + 10, '1 "', color='white', fontsize=25) + + cbar = plt.colorbar() + cbar.ax.tick_params(labelsize=ColorbarFont) + plt.figure(1) + plt.title('$S$', fontsize=TitleFont) + plt.imshow(TrueS, cmap=cm.gist_stern, interpolation='nearest') + plt.plot(ys, xs, 'w.', ms = 2) + plt.axis('off') + plt.xlim(xmax=ns1) + plt.ylim(ymax=ns2) + plt.xlim(xmin=0) + plt.ylim(ymin=0) + if delta_pix > 0: + plt.plot(XXarcs, XYarcs, 'w', linewidth=3) + plt.plot(YXarcs, YYarcs, 'w', linewidth=3) + plt.text(ns1 / 10 + 5, ns2 / 10 + 10, '1 "', color='white', fontsize=25) + cbar = plt.colorbar() + cbar.ax.tick_params(labelsize=ColorbarFont) + plt.figure(2) + plt.title('$S-\~S$', fontsize=TitleFont) + diff = (TrueS - S) + plt.imshow(diff, cmap=cm.gist_stern, interpolation='nearest') + plt.plot(ys, xs, 'w.', ms = 2) + plt.axis('off') + plt.xlim(xmax=ns1) + plt.ylim(ymax=ns2) + plt.xlim(xmin=0) + plt.ylim(ymin=0) + if delta_pix > 0: + plt.plot(XXarcs, XYarcs, 'w', linewidth=3) + plt.plot(YXarcs, YYarcs, 'w', linewidth=3) + plt.text(ns1 / 10 + 5, ns2 / 10 + 10, '1 "', color='white', fontsize=25) + cbar = plt.colorbar() + cbar.ax.tick_params(labelsize=ColorbarFont) + ####Lensed source + plt.figure(3) + plt.title('$HFS$', fontsize=TitleFont) + plt.imshow(TrueFS, cmap=cm.gist_stern, interpolation='nearest') + plt.plot(y, x, 'w.', ms = 2) + if delta_pix > 0: + plt.plot(XXarc, XYarc, 'w', linewidth=3) + plt.plot(YXarc, YYarc, 'w', linewidth=3) + plt.text(n1 / 10 + 5, n2 / 10 + 10, '1 "', color='white', fontsize=25) + plt.axis('off') + plt.xlim(xmax=n1) + plt.ylim(ymax=n2) + plt.xlim(xmin=0) + plt.ylim(ymin=0) + cbar = plt.colorbar() + cbar.ax.tick_params(labelsize=ColorbarFont) + plt.figure(4) + plt.title('$HF\~S$', fontsize=TitleFont) + plt.imshow((FS), vmin=np.min(TrueFS), vmax=np.max(TrueFS), cmap=cm.gist_stern, interpolation='nearest') + plt.plot(y, x, 'w.', ms = 2) + if delta_pix > 0: + plt.plot(XXarc, XYarc, 'w', linewidth=3) + plt.plot(YXarc, YYarc, 'w', linewidth=3) + plt.text(n1 / 10 + 5, n2 / 10 + 10, '1 "', color='white', fontsize=25) + plt.axis('off') + plt.xlim(xmax=n1) + plt.ylim(ymax=n2) + plt.xlim(xmin=0) + plt.ylim(ymin=0) + cbar = plt.colorbar() + cbar.ax.tick_params(labelsize=ColorbarFont) + plt.figure(5) + plt.title('$HFS-HF\~S$', fontsize=TitleFont) + plt.imshow((TrueFS - FS), cmap=cm.gist_stern, interpolation='nearest') + plt.plot(y, x, 'w.', ms = 2) + plt.axis('off') + plt.xlim(xmax=n1) + plt.ylim(ymax=n2) + plt.xlim(xmin=0) + plt.ylim(ymin=0) + if delta_pix > 0: + plt.plot(XXarc, XYarc, 'w', linewidth=3) + plt.plot(YXarc, YYarc, 'w', linewidth=3) + plt.text(n1 / 10 + 5, n2 / 10 + 10, '1 "', color='white', fontsize=25) + cbar = plt.colorbar() + cbar.ax.tick_params(labelsize=ColorbarFont) + ###Galaxy + plt.figure(6) + plt.title('$HG$', fontsize=TitleFont) + plt.imshow((TrueG), vmin=np.min(TrueG), vmax=np.max(TrueG), cmap=cm.gist_stern, interpolation='nearest') + plt.plot(y, x, 'w.', ms = 2) + plt.axis('off') + plt.xlim(xmax=n1) + plt.ylim(ymax=n2) + plt.xlim(xmin=0) + plt.ylim(ymin=0) + if delta_pix > 0: + plt.plot(XXarc, XYarc, 'w', linewidth=3) + plt.plot(YXarc, YYarc, 'w', linewidth=3) + plt.text(n1 / 10 + 5, n2 / 10 + 10, '1 "', color='white', fontsize=25) + cbar = plt.colorbar() + cbar.ax.tick_params(labelsize=ColorbarFont) + plt.figure(12) + plt.title('$H\~G$', fontsize=TitleFont) + plt.imshow((G), vmin=np.min(TrueG), vmax=np.max(TrueG), cmap=cm.gist_stern, interpolation='nearest') + plt.plot(y, x, 'w.', ms = 2) + plt.axis('off') + plt.xlim(xmax=n1) + plt.ylim(ymax=n2) + plt.xlim(xmin=0) + plt.ylim(ymin=0) + if delta_pix > 0: + plt.plot(XXarc, XYarc, 'w', linewidth=3) + plt.plot(YXarc, YYarc, 'w', linewidth=3) + plt.text(n1 / 10 + 5, n2 / 10 + 10, '1 "', color='white', fontsize=25) + cbar = plt.colorbar() + cbar.ax.tick_params(labelsize=ColorbarFont) + plt.figure(7) + plt.title('$HG-H\~G$', fontsize=TitleFont) + plt.imshow((TrueG - G), cmap=cm.gist_stern, interpolation='nearest') + plt.plot(y, x, 'w.', ms = 2) + plt.axis('off') + plt.xlim(xmax=n1) + plt.ylim(ymax=n2) + plt.xlim(xmin=0) + plt.ylim(ymin=0) + if delta_pix > 0: + plt.plot(XXarc, XYarc, 'w', linewidth=3) + plt.plot(YXarc, YYarc, 'w', linewidth=3) + plt.text(n1 / 10 + 5, n2 / 10 + 10, '1 "', color='white', fontsize=25) + cbar = plt.colorbar() + cbar.ax.tick_params(labelsize=ColorbarFont) + ###Image + plt.figure(8) + plt.title('$Y$', fontsize=TitleFont) + plt.imshow(Y, cmap=cm.gist_stern, interpolation='nearest') + plt.plot(y, x, 'w.', ms = 2) + plt.axis('off') + plt.xlim(xmax=n1) + plt.ylim(ymax=n2) + plt.xlim(xmin=0) + plt.ylim(ymin=0) + if delta_pix > 0: + plt.plot(XXarc, XYarc, 'w', linewidth=3) + plt.plot(YXarc, YYarc, 'w', linewidth=3) + plt.text(n1 / 10 + 5, n2 / 10 + 10, '1 "', color='white', fontsize=25) + cbar = plt.colorbar() + cbar.ax.tick_params(labelsize=ColorbarFont) + plt.figure(9) + plt.title('$H\~G+HF\~S$', fontsize=TitleFont) + plt.imshow(FS + FG, cmap=cm.gist_stern, interpolation='nearest') + plt.plot(y, x, 'w.', ms = 2) + plt.axis('off') + plt.xlim(xmax=n1) + plt.ylim(ymax=n2) + plt.xlim(xmin=0) + plt.ylim(ymin=0) + if delta_pix > 0: + plt.plot(XXarc, XYarc, 'w', linewidth=3) + plt.plot(YXarc, YYarc, 'w', linewidth=3) + plt.text(n1 / 10 + 5, n2 / 10 + 10, '1 "', color='white', fontsize=25) + cbar = plt.colorbar() + cbar.ax.tick_params(labelsize=ColorbarFont) + plt.figure(10) + plt.title('$Y-H\~G-HF\~S$', fontsize=TitleFont) + plt.imshow(Y - FS - FG, cmap=cm.gist_stern, interpolation='nearest', vmin=-5 * sigma, + vmax=5 * sigma) # slit.fft_convolve(Im,PSF) + plt.plot(y, x, 'w.', ms = 2) + plt.axis('off') + plt.xlim(xmax=n1) + plt.ylim(ymax=n2) + plt.xlim(xmin=0) + plt.ylim(ymin=0) + if delta_pix > 0: + plt.plot(XXarc, XYarc, 'w', linewidth=3) + plt.plot(YXarc, YYarc, 'w', linewidth=3) + plt.text(n1 / 10 + 5, n2 / 10 + 10, '1 "', color='white', fontsize=25) + cbar = plt.colorbar() + cbar.ax.tick_params(labelsize=ColorbarFont) + plt.show() + return 0 \ No newline at end of file diff --git a/SLIT/wave_transform.py b/SLIT/old/wave_transform.py similarity index 91% rename from SLIT/wave_transform.py rename to SLIT/old/wave_transform.py index ed28a82..426fdd1 100755 --- a/SLIT/wave_transform.py +++ b/SLIT/old/wave_transform.py @@ -47,7 +47,7 @@ def wave_transform(img, lvl, Filter = 'Bspline', newwave = 1, convol2d = 0): if np.size(sh) ==3: mn = np.min(sh) wave = np.zeros([lvl+1,sh[1], sh[1],mn]) - for h in np.linspace(0,mn-1, mn): + for h in range(mn): if mn == sh[0]: wave[:,:,:,h] = wave_transform(img[h,:,:],lvl+1, Filter = Filter) else: @@ -64,15 +64,15 @@ def wave_transform(img, lvl, Filter = 'Bspline', newwave = 1, convol2d = 0): h = np.array(h) if n+2**(lvl-1)*(n-1) >= np.min([n1,n2])/2.: - lvl = np.int_(np.log2((n1-1)/(n-1.))+1) + lvl = int(np.log2((n1-1)/(n-1.))+1) c = img ## wavelet set of coefficients. wave = np.zeros([lvl+1,n1,n2]) - for i in np.linspace(0,lvl-1,lvl): + for i in range(lvl): newh = np.zeros((1,n+(n-1)*(2**i-1))) - newh[0,np.int_(np.linspace(0,np.size(newh)-1,len(h)))] = h + newh[0, np.linspace(0,np.size(newh)-1,len(h), dytpe=int)] = h H = np.dot(newh.T,newh) ######Calculates c(j+1) @@ -121,10 +121,10 @@ def iuwt(wave, convol2d =0): cJ = np.copy(wave[lvl-1,:,:]) - for i in np.linspace(1,lvl-1,lvl-1): + for i in range(1, lvl): newh = np.zeros((1,n+(n-1)*(2**(lvl-1-i)-1))) - newh[0,np.int_(np.linspace(0,np.size(newh)-1,len(h)))] = h + newh[0, np.linspace(0, np.size(newh)-1,len(h), dtype=int)] = h H = np.dot(newh.T,newh) ###### Line convolution diff --git a/SLIT/tools.py b/SLIT/tools.py index 4c05755..53db83c 100755 --- a/SLIT/tools.py +++ b/SLIT/tools.py @@ -1,21 +1,81 @@ +import os import numpy as np import matplotlib.pyplot as plt -import pyfits as pf -from scipy import signal as scp -import gaussian as gs -import scipy.ndimage.filters as sc -import scipy.ndimage.filters as med -import scipy.signal as cp - -def MOM(A, B, levelA, levelB): - A = A[:-1,:,:] - B = B[:-1,:,:] - levelA = levelA[:-1,:,:] - levelB = levelB[:-1,:,:] - Amax = np.max(A[levelA!=0]/levelA[levelA!=0]) - Bmax = np.max(B[levelB!=0]/levelB[levelB!=0]) - k = np.min([Amax, Bmax]) - return k+0.1*np.abs(Amax-Bmax) +import astropy.io.fits as pf +import scipy.signal as scs +import scipy.ndimage.filters as scf +from mpl_toolkits.axes_grid1 import make_axes_locatable + +from SLIT import transform as tr + +# try: +# import pysap +# except ImportError: +# pysap_installed = False +# else: +# pysap_installed = True +pysap_installed = False + +# TODO : terminate proper PySAP inegration (i.e. manage the 'pysap_transform' +# object returned by wave_transform(), then pass it to iuwt()) + + +def wave_transform(img, lvl, Filter='Bspline', newwave=1, convol2d=0, verbose=False): + original_warning = "--> using original wavelet algorithm instead" + + if pysap_installed: + if newwave == 0: + coeffs, pysap_transform = tr.uwt_pysap(img, lvl, Filter=Filter) + else: + if verbose: + print("WARNING : PySAP does not support 2nd gen starlet") + print(original_warning) + coeffs = tr.uwt_original(img, lvl, Filter='Bspline', + newwave=newwave, convol2d=convol2d) + pysap_transform = None + else: + if verbose: + print("WARNING : PySAP not installed or not found") + print(original_warning) + coeffs = tr.uwt_original(img, lvl, Filter='Bspline', + newwave=newwave, convol2d=convol2d) + pysap_transform = None + return coeffs, pysap_transform + +def iuwt(wave, newwave=1, convol2d=0, pysap_transform=None, verbose=False): + original_warning = "--> using original transform algorithm instead" + + if pysap_installed: + if newwave == 0: + if pysap_transform is None: + raise RuntimeError("PySAP transform required for synthesis") + recon = tr.iuwt_pysap(wave, pysap_transform, fast=True) + else: + if verbose: + print("WARNING : PySAP does not support 2nd gen starlet") + print(original_warning) + coeffs = tr.iuwt_original(wave, convol2d=convol2d, newwave=newwave, fast=True) + + else: + if verbose: + print("WARNING : PySAP not installed or not found") + print(original_warning) + recon = tr.iuwt_original(wave, convol2d=convol2d, newwave=newwave) + return recon + +def MOM(S, G, levelS, levelG): + S = S[:-1,:,:] + G = G[:-1,:,:] + levelS = levelS[:-1,:,:] + levelG = levelG[:-1,:,:] + + sel = ((levelS!=0)) + + Smax = np.max(np.abs(S[sel])/levelS[sel]) + Gmax = np.max(np.abs(G[levelG!=0])/levelG[levelG!=0]) + + k = np.min([Smax, Gmax]) + return k+0.001*np.abs(Smax-Gmax) def MAD(x,n=3): ##DESCRIPTION: @@ -30,8 +90,9 @@ def MAD(x,n=3): ##OUTPUTS: ## -S: the source light profile. ## -FS: the lensed version of the estimated source light profile - x = wave_transform(x, np.int(np.log2(x.shape[0])))[0,:,:] - meda = med.median_filter(x,size = (n,n)) + coeffs, _ = wave_transform(x, np.int(np.log2(x.shape[0]))) + x = coeffs[0,:,:] + meda = scf.median_filter(x,size = (n,n)) medfil = np.abs(x-meda)#np.median(x)) sh = np.shape(x) sigma = 1.48*np.median((medfil)) @@ -39,7 +100,8 @@ def MAD(x,n=3): def MAD_box(x, tau): n1,n2 = x.shape - xw = wave_transform(x,2)[0,:,:] + coeffs, _ = wave_transform(x,2) + xw, _ = coeffs[0,:,:] winsize = 6 xw_pad = np.pad(xw, ((winsize/2, winsize/2),(winsize/2, winsize/2)), mode = 'symmetric') @@ -67,7 +129,8 @@ def MAD_poisson(x,tau,lvl): x0 = np.copy(x) def transform(i): - return wave_transform(i,lvl) + coeffs, _ = wave_transform(i,lvl) + return coeffs levels = level(n1,n2,lvl)*MAD(x) new_x = np.copy(x) new_x, y = mr_filter(new_x,levels, 8, 20, transform, iuwt, MAD(x), lvl = lvl) @@ -84,10 +147,10 @@ def level_poisson(n1,n2, lvl,transform,sigma): levels = np.zeros(wave_dirac.shape) for i in range(lvl): if np.size(sigma.shape) > 2: - lvlso = (scp.fftconvolve(sigma[i, :, :] ** 2, wave_dirac[i, :, :] ** 2, + lvlso = (scs.fftconvolve(sigma[i, :, :] ** 2, wave_dirac[i, :, :] ** 2, mode='same')) else: - lvlso = scp.fftconvolve(sigma ** 2, wave_dirac[i,:,:] ** 2, + lvlso = scs.fftconvolve(sigma ** 2, wave_dirac[i,:,:] ** 2, mode='same') levels[i, :, :] = np.sqrt(np.abs(lvlso)) @@ -95,7 +158,6 @@ def level_poisson(n1,n2, lvl,transform,sigma): return levels def Forward_Backward(Y, X, F_op, I_op, transform, inverse, mu, reg, pos = 1, subiter = 0): - R = mu*I_op(Y-F_op(X)) Xnew = np.copy(X+R) Xnew = inverse(reg(transform(Xnew))) @@ -114,9 +176,9 @@ def SDR(X, Y): def Res(X,Y,sigma): return np.sqrt(np.sum(((X-Y)/sigma)**2)/X.size)#np.std((X-Y)**2/sigma**2) - def FISTA(Y, alphaX, F_op, I_op, mu, ts, csi, reg, transform, inverse, pos = 1, mask = 1): S = inverse(alphaX) + # S = inverse(csi) # isn't it the standard FISTA behaviour ? R = mu*I_op(Y-F_op(S)*mask) alpha = transform(R)+csi @@ -135,9 +197,10 @@ def Soft(X, level, k, supp =1, Kill = 0): Xnew[-1,:,:] = 0 else: Xnew[-1, :, :] = X[-1,:,:] - + #print(Xnew.shape, supp.shape) - # Xnew = Xnew*supp + Xnew = Xnew*supp + return Xnew @@ -152,8 +215,10 @@ def level(n1, n2, lvl): ## -levels: units of noise levels at each scale and location of a starlet transform dirac = np.zeros((n1, n2)) # lvl = np.int(np.log2(n1)) - dirac[n1 / 2, n2 / 2] = 1 - wave_dirac = wave_transform(dirac, lvl, newwave=0) + + dirac[int(n1 / 2), int(n2 / 2)] = 1 + + wave_dirac, _ = wave_transform(dirac, lvl, newwave=0) wave_sum = np.sqrt(np.sum(np.sum(wave_dirac ** 2, 1), 1)) @@ -163,7 +228,7 @@ def level(n1, n2, lvl): def Soft_Threshold(X, transform, inverse, level, k, supp =1, Kill = 0): X = transform(X) - alpha = wave_transform(X,Xw.shape[0],newwave = 0) + alpha, _ = wave_transform(X,Xw.shape[0],newwave = 0) M = np.zeros(alpha.shape) M[np.abs(alpha)-level*k>0] = 1 M[0,:,:] = 0 @@ -194,7 +259,7 @@ def Hard(X, level, k, supp=1): def Hard_Threshold(X, transform, inverse, level, k, supp=1, M = [0]): Xw = transform(X) if np.sum(M) == 0: - alpha = wave_transform(X,Xw.shape[0],newwave = 0) + alpha, _ = wave_transform(X,Xw.shape[0],newwave = 0) M = np.zeros(alpha.shape) M[(np.abs(alpha)-level*k)>0] = 1 M[0,:,:] = 0 @@ -208,7 +273,7 @@ def Hard_Threshold(X, transform, inverse, level, k, supp=1, M = [0]): def mr_filter(Y, level, k, niter, transform, inverse, sigma, lvl = 6, Soft = 0, pos = 1, supp = 1): Xnew = 0 - alpha = wave_transform(Y, lvl, newwave=0) + alpha, _ = wave_transform(Y, lvl, newwave=0) M = np.zeros(alpha.shape) M[np.abs(alpha)-level*k>0] = 1 M[0,:,:] = 0 @@ -236,108 +301,6 @@ def mr_filter(Y, level, k, niter, transform, inverse, sigma, lvl = 6, Soft = 0, return (Xnew), M -def wave_transform(img, lvl, Filter = 'Bspline', newwave = 1, convol2d = 0): - - mode = 'nearest' - - lvl = lvl-1 - sh = np.shape(img) - if np.size(sh) ==3: - mn = np.min(sh) - wave = np.zeros([lvl+1,sh[1], sh[1],mn]) - for h in np.linspace(0,mn-1, mn): - if mn == sh[0]: - wave[:,:,:,h] = wave_transform(img[h,:,:],lvl+1, Filter = Filter) - else: - wave[:,:,:,h] = wave_transform(img[:,:,h],lvl+1, Filter = Filter) - return wave - - n1 = sh[1] - n2 = sh[1] - - if Filter == 'Bspline': - h = [1./16, 1./4, 3./8, 1./4, 1./16] - else: - h = [1./4,1./2,1./4] - n = np.size(h) - h = np.array(h) - - lvl = np.min([lvl,np.int(np.log2(n2))]) - - c = img - ## wavelet set of coefficients. - wave = np.zeros([lvl+1,n1,n2]) - - for i in np.linspace(0,lvl-1,lvl): - newh = np.zeros((1,n+(n-1)*(2**i-1))) - newh[0,np.int_(np.linspace(0,np.size(newh)-1,len(h)))] = h - H = np.dot(newh.T,newh) - - ######Calculates c(j+1) - ###### Line convolution - if convol2d == 1: - cnew = cp.convolve2d(c, H, mode='same', boundary='symm') - else: - cnew = sc.convolve1d(c,newh[0,:],axis = 0, mode =mode) - - ###### Column convolution - cnew = sc.convolve1d(cnew,newh[0,:],axis = 1, mode =mode) - - - - if newwave ==1: - ###### hoh for g; Column convolution - if convol2d == 1: - hc = cp.convolve2d(cnew, H, mode='same', boundary='symm') - else: - hc = sc.convolve1d(cnew,newh[0,:],axis = 0, mode = mode) - - ###### hoh for g; Line convolution - hc = sc.convolve1d(hc,newh[0,:],axis = 1, mode = mode) - - ###### wj+1 = cj-hcj+1 - wave[i,:,:] = c-hc - - else: - ###### wj+1 = cj-cj+1 - wave[i,:,:] = c-cnew - - - c = cnew - - wave[i+1,:,:] = c - - return wave - -def iuwt(wave, convol2d =0): - mode = 'nearest' - - lvl,n1,n2 = np.shape(wave) - h = np.array([1./16, 1./4, 3./8, 1./4, 1./16]) - n = np.size(h) - - cJ = np.copy(wave[lvl-1,:,:]) - - - for i in np.linspace(1,lvl-1,lvl-1): - - newh = np.zeros((1,n+(n-1)*(2**(lvl-1-i)-1))) - newh[0,np.int_(np.linspace(0,np.size(newh)-1,len(h)))] = h - H = np.dot(newh.T,newh) - - ###### Line convolution - if convol2d == 1: - cnew = cp.convolve2d(cJ, H, mode='same', boundary='symm') - else: - cnew = sc.convolve1d(cJ,newh[0,:],axis = 0, mode = mode) - ###### Column convolution - cnew = sc.convolve1d(cnew,newh[0,:],axis = 1, mode = mode) - - cJ = cnew+wave[lvl-1-i,:,:] - - return np.reshape(cJ,(n1,n2)) - - def plot_cube(cube): ##DESCRIPTION: ## Plotting device that displays layers of a cube in different subplot panels. @@ -357,3 +320,111 @@ def plot_cube(cube): plt.imshow(cube[k,:,:]); plt.colorbar() return None + +def Downsample(image, factor=1): + """ + resizes image with nx x ny to nx/factor x ny/factor + :param image: 2d image with shape (nx,ny) + :param factor: integer >=1 + :return: + """ + if factor < 1: + raise ValueError('scaling factor in re-sizing %s < 1' %factor) + f = int(factor) + nx, ny = np.shape(image) + if int(nx/f) == nx/f and int(ny/f) == ny/f: + small = image.reshape([int(nx/f), f, int(ny/f), f]).mean(3).mean(1) + return small + else: + raise ValueError("scaling with factor %s is not possible with grid size %s, %s" %(f, nx, ny)) + +def Upsample(image, factor): + factor = int(factor) + n1,n2 = image.shape + upimage = np.zeros((n1*factor, n2*factor)) + x,y = np.where(upimage==0) + upimage[x,y] = image[(x/factor),(y/factor)]/factor**2 + return upimage + + +def nice_colorbar(mappable, position='right', pad=0.1, size='5%', **kwargs): + kwargs.update({'position': position, 'pad': pad, 'size': size}) + ax = mappable.axes + divider = make_axes_locatable(ax) + cax = divider.append_axes(**kwargs) + return plt.colorbar(mappable, cax=cax) + +def save_steps(save_steps_dir, steps_to_save, input_image, suffix=""): + if not os.path.exists(save_steps_dir): + os.mkdir(save_steps_dir) + + # get vmax for color map levels + steps_array = np.array(steps_to_save) + vmin_src = np.min(steps_array[:, 0, :, :]) + vmax_src = np.max(steps_array[:, 0, :, :]) + vmin_img = np.min(steps_array[:, 1, :, :]) + vmax_img = np.max(steps_array[:, 1, :, :]) + vmax_res = np.max(np.abs(steps_array[:, 2, :, :])) + + # save animated plot for each step + + fig, axes = plt.subplots(1, 4, figsize=(24, 5)) + + step_str = ", step 0" + S0, FS0, res0 = steps_to_save[0] + + # fig, axes = plt.subplots(1, 4, figsize=(24, 5)) + ax = axes[0] + ax.set_title("$Y$") + im = ax.imshow(input_image, origin='lower', cmap='gist_stern') + nice_colorbar(im) + ax = axes[1] + ax.set_title("$FS$" + step_str) + im = ax.imshow(FS0, origin='lower', cmap='gist_stern', + vmin=vmin_img, vmax=vmax_img) + nice_colorbar(im) + ax = axes[2] + ax.set_title("$S$" + step_str) + im = ax.imshow(S0, origin='lower', cmap='gist_stern', + vmin=vmin_src, vmax=vmax_src) + nice_colorbar(im) + ax = axes[3] + ax.set_title("$Y - FS$" + step_str) + im = ax.imshow(input_image-FS0, origin='lower', cmap='bwr_r', + vmin=-vmax_res, vmax=vmax_res) + nice_colorbar(im) + + # for j, (Snew_j, FS_j) in enumerate(steps_to_save): + def one_step(j): + step_str = ", step {}".format(j) + S, FS, res = steps_to_save[j] + + ax = axes[1] + ax.set_title("$FS$" + step_str) + ax.imshow(FS, origin='lower', cmap='gist_stern', + vmin=vmin_img, vmax=vmax_img) + # nice_colorbar(im) + ax = axes[2] + ax.set_title("$S$" + step_str) + ax.imshow(S, origin='lower', cmap='gist_stern', + vmin=vmin_src, vmax=vmax_src) + # nice_colorbar(im) + ax = axes[3] + ax.set_title("$Y - FS$" + step_str) + ax.imshow(res, origin='lower', cmap='bwr_r', + vmin=-vmax_res, vmax=vmax_res) + # nice_colorbar(im) + + # fig_name = "SLIT_step{}.png".format(j) + # fig.savefig(os.path.join(save_steps_dir, fig_name), dpi=100) + # plt.close() + + from matplotlib.animation import FuncAnimation + + anim = FuncAnimation(fig, one_step, interval=500, frames=len(steps_to_save)) + + video_path = os.path.join(save_steps_dir, "SLIT_all_steps_{}.mp4".format(suffix)) + anim.save(video_path) + + print("Step-by-step timelapse saved to {}".format(video_path)) + diff --git a/SLIT/tools.pyc b/SLIT/tools.pyc deleted file mode 100644 index 0783816..0000000 Binary files a/SLIT/tools.pyc and /dev/null differ diff --git a/SLIT/transform.py b/SLIT/transform.py new file mode 100644 index 0000000..47bd552 --- /dev/null +++ b/SLIT/transform.py @@ -0,0 +1,165 @@ +import numpy as np +import scipy.signal as scs +import scipy.ndimage.filters as scf + + +def uwt_pysap(img, lvl, Filter='Bspline', n_omp_threads=None): + import pysap + + lvl -= 1 # TODO !!!!! + + def pysap2muscadet(a_list): + return np.asarray(a_list) + + nb_scale = lvl+1 # + 1 for the coarsest scale + + if Filter == 'Bspline': # = 1st starlet (2nd gen not yet implemented in PySAP) + + transform_name = 'BsplineWaveletTransformATrousAlgorithm' + + transf_kwargs = {} + if n_omp_threads is not None: + transf_kwargs['nb_procs'] = n_omp_threads + + # note that if 'n_omp_threads' is not provided, + # PySAP will automatically set it the + # max number of CPUs available minus 1 + + transform_obj = pysap.load_transform(transform_name) + transform = transform_obj(nb_scale=nb_scale, verbose=False, **transf_kwargs) + + else: + raise NotImplementedError("Only sarlet transform is supported for now") + + # set the image + transform.data = img + transform.analysis() + coeffs = transform.analysis_data + return pysap2muscadet(coeffs), transform + +def iuwt_pysap(wave, transform, fast=True): + import pysap + + def muscadet2pysap(a): + a_list = [] + for i in range(a.shape[0]): + a_list.append(a[i, :, :]) + return a_list + + if fast: + # for 1st gen starlet the reconstruction can be performed by summing all scales + recon = np.sum(wave, axis=0) + + else: + # use set the analysis coefficients + transform.analysis_data = muscadet2pysap(wave) + image = transform.synthesis() + recon = image.data + + return recon + +def uwt_original(img, lvl, Filter='Bspline', newwave=1, convol2d=0): + + mode = 'nearest' + + lvl = lvl-1 + sh = np.shape(img) + if np.size(sh) ==3: + mn = np.min(sh) + wave = np.zeros([lvl+1,sh[1], sh[1],mn]) + for h in range(mn): + if mn == sh[0]: + wave[:,:,:,h] = wave_transform(img[h,:,:],lvl+1, Filter = Filter) + else: + wave[:,:,:,h] = wave_transform(img[:,:,h],lvl+1, Filter = Filter) + return wave + + n1 = sh[1] + n2 = sh[1] + + if Filter == 'Bspline': + h = [1./16, 1./4, 3./8, 1./4, 1./16] + else: + h = [1./4,1./2,1./4] + n = np.size(h) + h = np.array(h) + + lvl = np.min( (lvl, int(np.log2(n2))) ) + + c = img + ## wavelet set of coefficients. + wave = np.zeros((lvl+1, n1, n2)) + + for i in range(lvl): + newh = np.zeros((1, n+(n-1)*(2**i-1))) + newh[0, np.linspace(0,np.size(newh)-1, len(h), dtype=int)] = h + + H = np.dot(newh.T,newh) + + ######Calculates c(j+1) + ###### Line convolution + if convol2d == 1: + cnew = scs.convolve2d(c, H, mode='same', boundary='symm') + else: + cnew = scf.convolve1d(c,newh[0,:],axis = 0, mode =mode) + + ###### Column convolution + cnew = scf.convolve1d(cnew,newh[0,:],axis = 1, mode =mode) + + + + if newwave ==1: + ###### hoh for g; Column convolution + if convol2d == 1: + hc = scs.convolve2d(cnew, H, mode='same', boundary='symm') + else: + hc = scf.convolve1d(cnew,newh[0,:],axis = 0, mode = mode) + + ###### hoh for g; Line convolution + hc = scf.convolve1d(hc,newh[0,:],axis = 1, mode = mode) + + ###### wj+1 = cj-hcj+1 + wave[i,:,:] = c-hc + + else: + ###### wj+1 = cj-cj+1 + wave[i,:,:] = c-cnew + + + c = cnew + + wave[i+1,:,:] = c + + return wave + +def iuwt_original(wave, convol2d=0, newwave=1, fast=True): + if newwave == 0 and fast: + # simply sum all scales, including the coarsest one + return np.sum(wave, axis=0) + + mode = 'nearest' + + lvl,n1,n2 = np.shape(wave) + h = np.array([1./16, 1./4, 3./8, 1./4, 1./16]) + n = np.size(h) + + cJ = np.copy(wave[lvl-1,:,:]) + + + for i in range(1, lvl): + + newh = np.zeros((1,n+(n-1)*(2**(lvl-1-i)-1))) + newh[0, np.linspace(0,np.size(newh)-1,len(h), dtype=int)] = h + H = np.dot(newh.T,newh) + + ###### Line convolution + if convol2d == 1: + cnew = scs.convolve2d(cJ, H, mode='same', boundary='symm') + else: + cnew = scf.convolve1d(cJ,newh[0,:],axis = 0, mode = mode) + ###### Column convolution + cnew = scf.convolve1d(cnew,newh[0,:],axis = 1, mode = mode) + + cJ = cnew+wave[lvl-1-i,:,:] + + return np.reshape(cJ,(n1,n2)) diff --git a/SLIT/wave_transform.pyc b/SLIT/wave_transform.pyc deleted file mode 100755 index 0c6b944..0000000 Binary files a/SLIT/wave_transform.pyc and /dev/null differ diff --git a/Test_SLIT.py b/Test_SLIT.py new file mode 100644 index 0000000..7d763e4 --- /dev/null +++ b/Test_SLIT.py @@ -0,0 +1,151 @@ +import astropy.io.fits as pf +import matplotlib.pyplot as plt +import numpy as np +import matplotlib.cm as cm + +import SLIT +import time +from scipy import signal as scp +import warnings +warnings.simplefilter("ignore") + +#Example of a run of the SLIT algorithm on simulated images. +#Here the first part of the file shows how simulations are generated. +#For users intereseted only in seeing the code run, have a look at the running SLIT section. +#The command line that builds the Fkappa operator is also of outmost importance. + + +###############################Simulation############################### +def SIE(x0,y0,n1,n2,b,beta,q,xc,theta): + kappa = np.zeros((n1,n2)) + x,y = np.where(kappa == 0) + eps = (1-q**2)/(1+q**2) + up = b**(beta-1) + pre = up/(2*(1-eps)**((beta-1)/2)) + count = 0 + theta = theta*np.pi/180. + for i in x: + Xr = (x[count]-x0)*np.cos(theta)-(y[count]-y0)*np.sin(theta) + Yr = (x[count]-x0)*np.sin(theta)+(y[count]-y0)*np.cos(theta) + kappa[x[count],y[count]] = pre/((xc**2.)/(1.-eps)+(Xr)**2.+((Yr)**2.)/q**2.)**((beta-1.)/2.) + + count += 1 + return kappa + +#Source light profile +newsource = pf.open('../Files/source.fits')[0].data +##N1,N2 are the numbers of pixels in the image plane. +nt1= 100 +nt2 = 100 +#Size ratio of the source to image number of pixels +size = 1 + +#PSF +PSF0 = pf.open('../Files/PSF.fits')[0].data +PSF = PSF0[1:,1:] +PSFconj = np.real(np.fft.ifft2(np.conjugate(np.fft.fft2(PSF0[:-1,:-1])))) +PSFconj=PSFconj/np.sum(PSFconj) +PSF = PSF/np.sum(PSF) + +## Lens mass distribution. +b = 1.53/0.05 +xc = 0.95 +q = 0.71 +betata = 2.1 +thetata = 25.2 +kappa = SIE(nt1/2.+50,nt2/2.+50,nt1+100,nt2+100,b,betata,q,xc, thetata) +#Mapping between lens and source IMPORTANT +Fkappa = SLIT.Lens.F(kappa, nt1,nt2, size,nt1/2.,nt2/2.) + + +#Generation of lensed source +I2 = SLIT.Lens.source_to_image(newsource, nt1 ,nt2 , Fkappa) + +#Noise levels +SNR = 500 +sigma = np.sqrt(np.sum(I2**2)/SNR/(nt1*nt2*size**2)) + +#Convolution by the PSF and generation of the final image +I2 = scp.fftconvolve(I2, PSF, mode = 'same') + +#Final simulated image +Image = I2+np.random.randn(nt1,nt2)*sigma + + +################################Running SLIT############################ +#Parameters +kmax = 5 +niter =100 +levels = [0] + +#Comment the following to have the level estimation routine run (takes more time) +levels = pf.open('../Files/Noise_levels_SLIT.fits')[0].data + +#Start clock +start = time.clock() + +#Running SLIT +sourcesl, Imsl = SLIT.SLIT(Image, Fkappa, kmax, niter, size, PSF, PSFconj, levels = levels, fb =1) + +#Stop clock +elapsed = (time.clock()-start) +print('execution time:', elapsed, 'seconds') + +#Reconstruction goodness +real_source = newsource +source_error = np.sum(np.abs(real_source[np.where(real_source!=0)] + -sourcesl[np.where(real_source!=0)])**2 + /real_source[np.where(real_source!=0)]**2)/(np.size( + np.where(real_source!=0))/2.) +image_chi2 = np.std(Image-Imsl)**2/sigma**2 +print('Residuals in source space', source_error) +print('Residuals in image space',image_chi2) + +#Display of results +for i in [1]: + plt.figure(2) + # plt.suptitle('FISTA: error per pixel on the source: '+str(source_error)+' image chi2:'+str(image_chi2)) + # plt.subplot(2,3,1) + plt.title('Source from SLIT') + plt.imshow((sourcesl), vmin = np.min(real_source), vmax = np.max(real_source),cmap = cm.gist_stern, interpolation = 'nearest') + plt.axis('off') + plt.colorbar() +# plt.subplot(2,3,2) + plt.figure(3) + plt.title('Original source') + plt.imshow(real_source, cmap = cm.gist_stern, interpolation = 'nearest') + plt.axis('off') + plt.colorbar() + # plt.subplot(2,3,3) + plt.figure(4) + plt.title('Lensed source') + plt.imshow(Image, cmap = cm.gist_stern, interpolation = 'nearest') + plt.axis('off') + plt.colorbar() + plt.figure(41) + plt.title('Reconstructed lensed source') + plt.imshow(Imsl, vmin = np.min(Image), vmax = np.max(Image), cmap = cm.gist_stern, interpolation = 'nearest') + plt.axis('off') + plt.colorbar() + # plt.subplot(2,3,4) + plt.figure(5) + plt.title('relative difference') + diff = (real_source-sourcesl)/real_source + diff[np.where(real_source==0)] = 0 + diff[np.where(diff>1)]= np.log(0.) + plt.imshow(np.abs(diff), vmax = 1., vmin = 0., cmap = cm.gist_stern, interpolation = 'nearest' ) + plt.axis('off') + plt.colorbar() + # plt.subplot(2,3,5) + plt.figure(6) + plt.title('difference with reconstructed lensed image') + plt.imshow(Image-Imsl, vmin = -5*sigma, vmax = 5*sigma, cmap = cm.gist_stern, interpolation = 'nearest') + plt.axis('off') + plt.colorbar() + # plt.subplot(2,3,6) + plt.figure(7) + plt.title('difference with true source') + plt.imshow((np.abs(real_source-sourcesl)), cmap = cm.gist_stern, interpolation = 'nearest') + plt.axis('off') + plt.colorbar() +plt.show() diff --git a/Test_SLIT_MCA.py b/Test_SLIT_MCA.py new file mode 100644 index 0000000..48e6700 --- /dev/null +++ b/Test_SLIT_MCA.py @@ -0,0 +1,201 @@ +from SLIT import Lens +import pyfits as pf +import matplotlib.pyplot as plt +import numpy as np +import matplotlib.cm as cm +from scipy import signal as scp +import SLIT as slit +import time +from scipy import signal as scp +import warnings +warnings.simplefilter("ignore") + +#Example of a run of the SLIT_MCA algorithm on simulated images. +#Here the first part of the file shows how simulations are generated. +#For users intereseted only in seeing the code run, have a look at the running SLIT_MCA section. +#The command line that builds the Fkappa operator is also of outmost importance. + + +###############################Simulation############################### +def SIE(x0,y0,n1,n2,b,beta,q,xc,theta): + kappa = np.zeros((n1,n2)) + x,y = np.where(kappa == 0) + eps = (1-q**2)/(1+q**2) + up = b**(beta-1) + pre = up/(2*(1-eps)**((beta-1)/2)) + count = 0 + theta = theta*np.pi/180. + for i in x: + Xr = (x[count]-x0)*np.cos(theta)-(y[count]-y0)*np.sin(theta) + Yr = (x[count]-x0)*np.sin(theta)+(y[count]-y0)*np.cos(theta) + kappa[x[count],y[count]] = pre/((xc**2.)/(1.-eps)+(Xr)**2.+((Yr)**2.)/q**2.)**((beta-1.)/2.) + + count += 1 + return kappa + +#Source light profile +newsource = pf.open('../Files/source.fits')[0].data +##N1,N2 are the numbers of pixels in the image plane. +nt1= 100 +nt2 = 100 +#Size ratio of the source to image number of pixels +size = 1 + +#PSF +PSF0 = pf.open('../Files/PSF.fits')[0].data +PSF = PSF0[1:,1:] +PSFconj = np.real(np.fft.ifft2(np.conjugate(np.fft.fft2(PSF0[:-1,:-1])))) +PSFconj=PSFconj/np.sum(PSFconj) +PSF = PSF/np.sum(PSF) + +## Lens mass distribution. +b = 1.53/0.05 +xc = 0.95 +q = 0.71 +betata = 2.1 +thetata = 25.2 +kappa = SIE(nt1/2.+50,nt2/2.+50,nt1+100,nt2+100,b,betata,q,xc, thetata) +#Mapping between lens and source IMPORTANT +Fkappa = slit.Lens.F(kappa, nt1,nt2, size,nt1/2.,nt2/2.) + +#Lens galaxy light profile +gal0 = pf.open('../Files/Galaxy.fits')[0].data + +#Generation of lensed source +I2 = slit.Lens.source_to_image(newsource, nt1 ,nt2 , Fkappa) +HI2 = scp.fftconvolve(I2, PSF.astype(float), mode = 'same') + +#Noise levels +SNR = 500 +sigma = np.sqrt(np.sum(I2**2)/SNR/(nt1*nt2*size**2)) + +#Convolution of the observed image +simu = scp.fftconvolve(gal0.astype(float)+I2, PSF.astype(float), mode = 'same') +#Sotring the convolved lens light profile: +gal = scp.fftconvolve(gal0.astype(float), PSF.astype(float), mode = 'same') + +#Final simulated image +Image = simu+np.random.randn(nt1,nt2)*sigma + +lensed = slit.lens_one(Fkappa, nt1,nt2, size) +Test = slit.Lens.image_to_source(I2+gal, size, Fkappa, lensed = lensed) + +plt.imshow(Image, cmap = cm.gist_stern, interpolation = 'nearest') +plt.show() +plt.imshow(Test, cmap = cm.gist_stern, interpolation = 'nearest') +plt.show() + +hdus = pf.PrimaryHDU(Image) +lists = pf.HDUList([hdus]) +lists.writeto('Image.fits', clobber=True) + +################################Running SLIT############################ +#Parameters +kmax = 5 +niter =100 +riter =100 +levels = [0] + +#Comment the following to have the level estimation routine run (takes more time) +levels = pf.open('../Files/Noise_levels_SLIT_MCA.fits')[0].data + +#Start clock +start = time.clock() + +#Running SLIT_MCA +S, FS, G = slit.SLIT_MCA(Image, Fkappa, kmax, niter,riter, size,PSF, PSFconj, levels = levels) + +#Stop clock +elapsed = (time.clock()-start) +print('execution time:', elapsed, 'seconds') + + +real_source = newsource + +source_error = np.sum(np.abs(real_source[np.where(real_source!=0)] + -S[np.where(real_source!=0)])**2 + /real_source[np.where(real_source!=0)]**2)/(np.size( + np.where(real_source!=0))/2.) + +image_chi2 = np.std(Image-FS-G)**2/sigma**2 +print('Residuals in source space', source_error) +print('Residuals in image space',image_chi2) + +for i in [1]: + ###Source + + plt.figure(0) + plt.title('Source from SLIT') + plt.imshow((S), vmin = np.min(real_source), vmax = np.max(real_source), cmap = cm.gist_stern, interpolation = 'nearest') + plt.axis('off') + plt.colorbar() + + plt.figure(1) + plt.title('Original image of the source') + plt.imshow(real_source, cmap = cm.gist_stern, interpolation = 'nearest') + plt.axis('off') + plt.colorbar() + + plt.figure(2) + plt.title('relative difference') + diff = (real_source-S) + plt.imshow((np.abs(diff)), cmap = cm.gist_stern, interpolation = 'nearest') + plt.axis('off') + plt.colorbar() + ####Lensed source + plt.figure(3) + plt.title('Original lensed galaxy') + plt.imshow(HI2, cmap = cm.gist_stern, interpolation = 'nearest') + plt.axis('off') + plt.colorbar() + + plt.figure(4) + plt.title('reconstructed lensed source') + plt.imshow((FS), vmin = np.min(I2), vmax = np.max(I2), cmap = cm.gist_stern, interpolation = 'nearest') + plt.axis('off') + plt.colorbar() + + plt.figure(5) + plt.title('error on the source in image plane') + plt.imshow((HI2-FS), cmap = cm.gist_stern, interpolation = 'nearest') + plt.axis('off') + plt.colorbar() + ###Galaxy + plt.figure(6) + plt.title('Original galaxy') + plt.imshow((gal0), cmap = cm.gist_stern, interpolation = 'nearest') + plt.axis('off') + plt.colorbar() + + plt.figure(12) + plt.title('Estimated Galaxy') + plt.imshow((G), vmin = np.min(gal0), vmax = np.max(gal0), cmap = cm.gist_stern, interpolation = 'nearest') + plt.axis('off') + plt.colorbar() + + plt.figure(7) + plt.title('Error on the galaxy') + plt.imshow((gal-G), cmap = cm.gist_stern, interpolation = 'nearest') + plt.axis('off') + plt.colorbar() + ###Image + plt.figure(8) + plt.title('Image') + plt.imshow(Image, cmap = cm.gist_stern, interpolation = 'nearest') + plt.axis('off') + plt.colorbar() + + plt.figure(9) + plt.title('Reconstructed image') + plt.imshow(FS+G, cmap = cm.gist_stern, interpolation = 'nearest') + plt.axis('off') + plt.colorbar() + + plt.figure(10) + plt.title('difference with reconstructed image') + plt.imshow(Image-FS-G,cmap = cm.gist_stern, interpolation = 'nearest', vmin = -5*sigma, vmax = 5*sigma)#slit.fft_convolve(Im,PSF) + plt.axis('off') + plt.colorbar() + + +plt.show() diff --git a/Tests/Test_center.pyc b/Tests/Test_center.pyc deleted file mode 100644 index 7a5c475..0000000 Binary files a/Tests/Test_center.pyc and /dev/null differ diff --git a/Tests/gaussian.pyc b/Tests/gaussian.pyc deleted file mode 100644 index a923ee4..0000000 Binary files a/Tests/gaussian.pyc and /dev/null differ diff --git a/build/lib/SLIT/Lens.py b/build/lib/SLIT/Lens.py deleted file mode 100644 index 5481004..0000000 --- a/build/lib/SLIT/Lens.py +++ /dev/null @@ -1,237 +0,0 @@ -import numpy as np -import matplotlib.pyplot as plt -import pyfits as pf -import scipy.signal as scp -import warnings -warnings.simplefilter("ignore") - - -#Tool box for lensing -def SIS(x0,y0,n1,n2,Re): - kappa = np.zeros((n1,n2)) - x,y = np.where(kappa == 0) - count = 0 - for i in x: - kappa[x[count],y[count]] = Re/(2*np.sqrt((x[count]-x0)**2+(y[count]-y0)**2)) - - count += 1 - if np.isfinite(kappa[x0,y0]) == False: - kappa[x0,y0] = 1 - - return kappa - -def SIE_xy(x,y,x0,y0,b,beta,q,xc,theta): - eps = (1-q**2)/(1+q**2) - up = b**(beta-1) - pre = up/(2*(1-eps)**((beta-1)/2)) - count = 0 - theta = theta*np.pi/180. - Xr = (x-x0)*np.cos(theta)-(y-y0)*np.sin(theta) - Yr = (x-x0)*np.sin(theta)+(y-y0)*np.cos(theta) - kappa = pre/((xc**2.)/(1.-eps)+(Xr)**2.+((Yr)**2.)/q**2.)**((beta-1.)/2.) - - return kappa - -def SIE(x0,y0,n1,n2,b,beta,q,xc,theta): - kappa = np.zeros((n1,n2)) - x,y = np.where(kappa == 0) - x2d = np.reshape(x, (n1,n2)) - y2d = np.reshape(y, (n1,n2)) - kappa = SIE_xy(x2d,y2d,x0,y0,b,beta,q,xc,theta) - return kappa - - -def alpha_def(kappa, n1,n2,x0,y0,extra): - #Computes the deflection angle of a single photon at coordinates theta in the source plane and a lens - #mass distribution kappa - - nk1,nk2 = np.shape(kappa) - x0+=extra/2. - y0+=extra/2. - #Coordonnees de la grille de l'espace image - [x,y] = np.where(np.zeros([nk1,nk2])==0) - [xk,yk] = np.where(np.zeros([nk1,nk2])==0) - - xc = np.reshape((x)-x0,(nk1,nk2)) - yc = np.reshape((y)-y0,(nk1,nk2)) - xkc = np.reshape((xk)-(nk1/2.),(nk1,nk2)) - ykc = np.reshape((yk)-(nk2/2.),(nk1,nk2)) - - - r = (xc**2+yc**2) - rk = np.sqrt(xkc**2+ykc**2) - lx,ly = np.where(r==0) - tabx = np.reshape((xc)/r,(nk1,nk2)) - taby = np.reshape((yc)/r,(nk1,nk2)) - tabx[lx,ly]=0 - taby[lx,ly]=0 - - l = 0 - - - kappa = kappa.astype(float) - tabx = tabx.astype(float) - -# kappa[rk>(nk1)/2.] = 0 - - intex = scp.fftconvolve(tabx, (kappa), mode = 'same')/np.pi - intey = scp.fftconvolve(taby, (kappa), mode = 'same')/np.pi - - - return intex[x0-(n1)/2.:x0+(n1)/2,y0-(n2)/2.:y0+(n2)/2.],intey[x0-(n1)/2.:x0+(n1)/2,y0-(n2)/2.:y0+(n2)/2.] - -def beta(kappa,theta): - #Computes beta - beta = theta-alpha(theta,kappa) - return beta - -def theta(alpha, beta): - #Computes beta - theta = beta+alpha - return beta - -def F(kappa, nt1,nt2, size, x0, y0, extra=100, x_shear = 0, y_shear = 0, alpha_x_in = [-99], alpha_y_in = [-99]): - # Theta positions for each pixel in beta - - - if np.sum(alpha_x_in) != [-99]: - alpha_x = alpha_x_in - alpha_y = alpha_y_in - else: - - nk1,nk2 = np.shape(kappa) - - alpha_x,alpha_y = alpha_def(kappa,nt1,nt2,x0,y0,extra) - - - alpha_x = alpha_x+x_shear - alpha_y = alpha_y+y_shear - - - na1,na2 = np.shape(alpha_x) - xa,ya = np.where(np.zeros((na1,na2)) == 0) - # xa = xa-(x0+extra/2) - #ya = ya-(y0+extra/2) - - nb1=nt1*size - nb2=nt2*size - xb, yb = np.where(np.zeros((nb1,nb2))==0) - - #Scaling of the source grid - - #Scaling of the deflection grid - xa = xa*(np.float(nt1)/np.float(na1))#-0.68 - ya = ya*(np.float(nt2)/np.float(na2))#-0.68 - #Setting images coordinates in 2d - xa2d = np.reshape(xa,(na1,na2)) - ya2d = np.reshape(ya,(na1,na2)) - - - - F2 = [] - for i in range(np.size(xb)): - #Deflection of photons emitted in xb[i],yb[i] - theta_x = (xb[i])*(np.float(nt1)/np.float(nb1))+alpha_x - theta_y = (yb[i])*(np.float(nt2)/np.float(nb2))+alpha_y - #Matching of arrivals with pixels in image plane - xprox = np.int_(np.abs((xa2d-theta_x)*2)) - yprox = np.int_(np.abs((ya2d-theta_y)*2)) - - - if np.min(xprox+yprox) <1.5: - loc2 = np.where((xprox+yprox)==np.min(xprox+yprox))# - else: - loc2 = [] - if (np.size(loc2)==0): - - F2.append([0]) - else: - F2.append((np.array(loc2))-1) - return F2 - - -def source_to_image(Source, nt1,nt2, theta, ones = 1): - # Source: Image of the source in the source plane - # n1,n2: size in pixels of the postage stamp in image plane - # F: the coordinates of the lens mapping - F = (theta) - nb1,nb2 = np.shape(Source) - - if ones == 1: - onelens = source_to_image(np.ones(Source.shape), nt1,nt2, theta, ones = 0) - onelens[np.where(onelens==0)]=1 - - else: - onelens = 1. - - - Image = np.zeros((nt1,nt2)) - xb,yb = np.where(np.zeros((nb1,nb2)) == 0) - - N = np.size(xb) - k=0 - for pos in F: - - if np.size(np.shape(pos)) != 1: - - Image[np.array(pos[0][np.where((pos[0][:] 1: - if np.sum(lensed) !=0: - if square == 0: - Source[xb[k],yb[k]] += np.sum(Image[np.array(pos[0][:]), - np.array(pos[1][:])])/np.max([1,np.size(pos[0][:])]) - else: - Source[xb[k], yb[k]] += np.sum((Image[np.array(pos[0][:]), - np.array(pos[1][:])] / np.max([1, np.size(pos[0][:])]))**2) - else: - Source[xb[k],yb[k]] += np.sum(Image[np.array(pos[0][:]), - np.array(pos[1][:])]) - if square == 1: - Source = np.sqrt(Source) - return Source - -def image_to_source_bound(Image, size,beta,lensed = 0): - # Image: postagestamp of the observed image - # nsize1,nsize2: size of the postagestamp in source plane - # F: lens mapping matrix - - F = (beta) - nt1,nt2 = np.shape(Image) - nb1 = nt1*size - nb2 = nt2*size - Source = np.zeros((nb1,nb2)) - xb,yb = np.where(Source == 0) - N = np.size(xb) - for k in range(N): - pos = F[k] - if np.size(np.shape(pos)) > 1: - if np.sum(lensed) !=0: - Source[xb[k],yb[k]] += np.sum(Image[np.array(pos[0][:]), - np.array(pos[1][:])])/np.max([1,np.size(pos[0][:])]) - else: - Source[xb[k],yb[k]] += np.sum(Image[np.array(pos[0][:]), - np.array(pos[1][:])]) - - return Source - diff --git a/build/lib/SLIT/Solve.py b/build/lib/SLIT/Solve.py deleted file mode 100644 index fab9a80..0000000 --- a/build/lib/SLIT/Solve.py +++ /dev/null @@ -1,694 +0,0 @@ -#from __future__ import division -import wave_transform as mw -import numpy as np -import matplotlib.pyplot as plt -import pyfits as pf -import matplotlib.cm as cm -from scipy import signal as scp -import scipy.ndimage.filters as med -import MuSCADeT as wine -from numpy import linalg as LA -import multiprocess as mtp -from pathos.multiprocessing import ProcessingPool as Pool -import Lens -import warnings -import tools -warnings.simplefilter("ignore") - -##SLIT: Sparse Lens Inversion Technique - -def SLIT(Y, Fkappa, kmax, niter, size, PSF, PSFconj, S0 = [0], levels = [0], scheme = 'FB', - mask = [0], lvl = 0, weightS = 1, noise = 'gaussian', tau = 0): - ##DESCRIPTION: - ## Function that estimates the source light profile from an image of a lensed source given the mass density profile. - ## - ##INPUTS: - ## -img: a 2-D image of a lensed source given as n1xn2 numpy array. - ## -Fkappa: an array giving the mapping between lens and source. This array is calculated from the lens mass density - ## using tools from SLIT.Lens - ## -kmax: the detection threshold in units of noise levels. We usualy set this value to 5 to get a 5 sigma - ## detection threshold. - ## -niter: maximal number of iterations of the algorithm. - ## -size: resoluution factor between lens and source grids such thathe size of the output source - ## will be n1sizexn2size - ## -PSF: the point spread function of the observation provided as a 2D array. - ## -PSFconj: The conjugate of the PSF. Usually computed via np.real(np.fft.ifft2(np.conjugate(np.fft.fft2(PSF0[:-1,:-1])))) - ## butthe user has to make sure that the conjugate is well centered. - ## - ##OPTIONS: - ## -levels: an array that contains the noise levels at each band of the wavelet decomposition of the source. - ## If not provided, the routine will compute the levels and save them in a fits file 'Noise_levels.fits' - ## so that they can be used at a later time. This option allows to save time when running the same - ## experiment several times. - ## -mask: an array of zeros and one with size ns1xns2. The zeros will stand for masked data. - ## - ##OUTPUTS: - ## -S: the source light profile. - ## -FS: the lensed version of the estimated source light profile - ## - ##EXAMPLE: - ## S,FS = SLIT(img, Fkappa, 5, 100, 1, PSF, PSFconj) - - n1,n2 = np.shape(Y) - # PSFconj = np.rot90(PSF, 2) - #Size of the source - ns1,ns2 = n1*size, n2*size - #Number of starlet scales in source plane - if lvl ==0: - lvl = np.int(np.log2(ns2)) - else: - lvl = np.min([lvl,np.int(np.log2(ns2))]) - - #Masking if required - if np.sum(mask) == 0: - mask = np.ones((n1,n2)) - img = Y*mask - - #Noise in image plane - sigma0 = MAD(Y) - if noise == 'poisson': - if tau ==0: - print('error: Give exposure time') - Y0 =np.copy(Y) - sigma = np.copy(sigma0) - Y = 2./tau*np.sqrt(tau*np.abs(Y)+tau*3./8.+sigma0)*np.sign(tau*Y+tau*3./8.+sigma0) - - - - - sigma0 = MAD(Y) - - - #Mapping of an all-at-one image to source plane - lensed = lens_one(Fkappa, n1,n2, size) - #estimation of the frame of the image in source plane - supp = np.zeros((lvl,lensed.shape[0],lensed.shape[1])) - supp[:,lensed/lensed ==1] =1 - - #Useful functions - def Finv_apply(I): - return Lens.image_to_source(I, size, Fkappa, lensed = lensed) - def Lens_op2(I): - return Lens.image_to_source(I, size, Fkappa, lensed = lensed, square = 1) - def F_apply(Si): - return Lens.source_to_image(Si, n1, n2,Fkappa) - def PSF_apply(i): - return scp.fftconvolve(i,PSF,mode = 'same') - def PSFT_apply(ii): - return scp.fftconvolve(ii,PSFconj,mode = 'same') - def transform(x): - return tools.wave_transform(x, lvl, newwave = 1) - def inverse(x): - return tools.iuwt(x) - - #Forward operator - def F_op(X): - return PSF_apply(F_apply(X)) - #Inverse operator - def I_op(X): - return Finv_apply(PSFT_apply(X)) - #Regularisation (Backward term) - def reg0(X): - return tools.Hard(X, transform, inverse,levels, (ks), supp=supp) - def reg00(X): - return tools.Hard_Threshold(X, transform, inverse,levels, (ks), supp=supp) - def reg1(X): - return tools.Soft(X, transform, inverse,levels*weightS, kmax, supp=supp) - def reg_filter(X): - return tools.mr_filter(X,levels,ks,20,transform, inverse, lvl = lvl) - #Noise simulations to estimate noise levels in source plane - if np.sum(levels)==0: - print('Calculating noise levels') - #levels = simulate_noise(n1,n2, sigma0, size, I_op, transform, lvl) - levels = level_source(n1,n2,sigma0,size,PSFconj, Lens_op2, lensed, lvl) - #Saves levels - hdus = pf.PrimaryHDU(levels) - lists = pf.HDUList([hdus]) - lists.writeto('Noise_levels.fits', clobber=True) - - -##Compute spectral norms - - op_norm = spectralNorm(ns1,ns2,20,1e-10,F_op,I_op) - wave_norm = spectralNorm(ns1,ns2,20,1e-10,transform,inverse) - nu = 0.5#op_norm**2/(2*wave_norm**2)-1./(mu) - mu = 1./(op_norm+wave_norm) - - if scheme == 'FB': - repeat =1 - else: - repeat = 2 - #Initialisation - - - Res1= [] - - tau = 0.5 - - for jr in range(repeat): - trans = (transform(I_op(Y))/levels)[:-1,:,:] - ks0 = np.max(trans[levels[:-1,:,:]!=0]) - ks=np.copy(ks0) - steps = (ks0-kmax)/(niter-5) - karg = np.log(kmax/ks0)/(niter-5.) - i = 0 - if np.sum(S0) == 0: - S=np.random.randn(ns1,ns2)*np.median(sigma0)*0 - else: - S = S0 - ts = 1 - csi = 0 - Res1= [] - Res2 = [] - - - - - alpha =transform(S) - - while i < niter: - print(i) - if scheme == 'FB': - ks = ks0*np.exp(i*karg) - ks = np.max([ks, kmax]) - S = tools.Forward_Backward(Y, S, F_op, I_op, mu, reg_filter, pos = 1) - S[S<0] = 0 - FS = F_op(S)*mask - - else: - alpha, csi, ts = tools.FISTA(Y, alpha, F_op, I_op, mu, ts, csi, reg1, transform, inverse, mask = mask) - S = inverse(alpha) - FS = F_op(S) - - - - - - #Convergence condition - Res1.append((np.std(Y-FS)**2)/np.median(sigma0)**2) - Res2.append(ks) - # ks = ks-steps - - - i = i+1 - - S[S<0] = 0 - -# alpha = transform(S) - weightS = 1./(1.+np.exp(-10.*(levels*kmax-alpha))) -# plt.show() - #Final reconstruction of the source - plt.plot(Res1, 'b'); plt.show() - plt.plot(Res2, 'r'); - plt.show() - if noise == 'poisson': - plt.subplot(211) - plt.title('S') - plt.imshow(S); plt.colorbar() - plt.show() - FS = F_op(S)*mask - return S, FS - - -#############################SLIT MCA for blended lenses############################ - - -def SLIT_MCA(Y, Fkappa, kmax, niter, riter, size,PSF, PSFconj, lvlg = 0, lvls = 0, levels = [0], mask = [0,0], Ginit=0): - ##DESCRIPTION: - ## Function that estimates the source and lens light profiles from an image of a - ## strong lens system - ## - ##INPUTS: - ## -img: a 2-D image of a lensed source given as n1xn2 numpy array. - ## -Fkappa: an array giving the mapping between lens and source. This array is calculated from the lens mass density - ## using tools from SLIT.Lens - ## -kmax: the detection threshold in units of noise levels. We usualy set this value to 5 to get a 5 sigma - ## detection threshold. - ## -niter: maximal number of iterations in the main loop over G. - ## -riter: maximal number of iterations in the inner loop over S. - ## -size: resoluution factor between lens and source grids such thathe size of the output source - ## will be n1sizexn2size - ## -PSF: the point spread function of the observation provided as a 2D array. - ## -PSFconj: The conjugate of the PSF. Usually computed via np.real(np.fft.ifft2(np.conjugate(np.fft.fft2(PSF0[:-1,:-1])))) - ## butthe user has to make sure that the conjugate is well centered. - ## - ##OPTIONS: - ## -levels: an array that contains the noise levels at each band of the wavelet decomposition of the source. - ## If not provided, the routine will compute the levels and save them in a fits file 'Noise_levels.fits' - ## so that they can be used at a later time. This option allows to save time when running the same - ## experiment several times. - ## -mask: an array of zeros and one with size ns1xns2. The zeros will stand for masked data. - ## -Ginit: Educated guedd for the lens galaxy light profile. if set to a 2D numpy array, the array will be used as - ## as an initialisation for G. - ## - ##OUTPUTS: - ## -S: the source light profile. - ## -G: the convolved lens light profile - ## -FS: the lensed version of the estimated source light profile - ## - ##EXAMPLE: - ## S,FS = SLIT(img, Fkappa, 5, 100, 1, PSF, PSFconj) - - #Shape of the image - n1,n2 = np.shape(Y) - #Initialisation of the source - ns1= n1*size - ns2 = n2*size - #Number of starlet scales in source and image planes - if lvlg ==0: - lvlg = np.int(np.log2(n2)) - else: - lvlg = np.min([lvlg,np.int(np.log2(n2))]) - lvls = lvlg - if lvls >np.int(np.log2(ns2)): - print('Error, too many wavelet levels for the source. Choose a smaller value for lvl') - exit - #Masking if required - if np.sum(mask) == 0: - mask = np.ones((n1,n2)) - Y = Y*mask - #Noise standard deviation in image plane - sigma0 = MAD(Y) - #Mapping of an all-at-one image - lensed = lens_one(Fkappa, n1,n2, size) - - - supp = np.zeros((lvls,lensed.shape[0],lensed.shape[1])) - supp[:,lensed/lensed ==1] =1 - - #Limits of the image plane in source plane - bound = mk_bound(Fkappa, n1,n2, size) - #Noise levels in image plane in starlet space - levelg = level(n1,n2, lvlg)*sigma0 - - - #Useful functions - def Finv_apply(I): - return Lens.image_to_source(I, size, Fkappa, lensed = lensed) - def F_apply(Si): - return Lens.source_to_image(Si, n1, n2,Fkappa) - def PSF_apply(i): - return scp.fftconvolve(i,PSF,mode = 'same') - def PSFT_apply(ii): - return scp.fftconvolve(ii,PSFconj,mode = 'same') - def transform(x): - return tools.wave_transform(x, lvlg) - def inverse(x): - return tools.iuwt(x) - - #Forward Source operator - def FS_op(X): - return PSF_apply(F_apply(X)) - #Inverse Source operator - def IS_op(X): - return Finv_apply(PSFT_apply(X)) - #Forward Lens operator - def FG_op(X): - return ((X)) - #Inverse Lens operator - def IG_op(X): - return ((X)) - #Regularisation (Backward term) - def regG0(X): - return tools.Hard_Threshold(X, transform, inverse, levelg*kG) - def regS0(X): - return tools.Hard_Threshold(X, transform, inverse, levels*kS) - def regS1(X): - return tools.Soft(X, transform, inverse, levels*kmax*weightS, supp = supp) - def regG1(X): - return tools.Soft(X, transform, inverse, levelg*(kmax)*weightG, supp = 1) - def reg_filter(X): - return tools.mr_filter(X, levelg*kG*sigma0, 20, transform, inverse, Soft = 0, pos = 1) - - #Noise simulations to estimate noise levels in source plane - if np.sum(levels)==0: - print('Calculating noise levels') - levels = simulate_noise(n1,n2, sigma0, size, IS_op, transform, lvls) - levels[:,lensed ==0] = np.max(levels*10) - #Saves levels - hdus = pf.PrimaryHDU(levels) - lists = pf.HDUList([hdus]) - lists.writeto('Noise_levels_MCA.fits', clobber=True) - - - - #Computationt of spectral norms - FS_norm = spectralNorm(ns1,ns2,20,1e-10,FS_op,IS_op) - Star_norm_im = spectralNorm(n1,n2,20,1e-10,transform,inverse) - Star_norm_s = spectralNorm(ns1,ns2,20,1e-10,transform,inverse) - muG = 1./(Star_norm_im**2) - muS = 1./(Star_norm_s*FS_norm)**2 - print(muS, muG) - - weightS = 1 - weightG = 1 - - #Reweighting loop - for it in range(3): - #Initialisations - FS = 0 - G = np.zeros((n1,n2)) - S = np.zeros((ns1,ns2)) - alphaS = transform(S) - csiS = np.copy(alphaS) - alphaG = transform(G) - csiG = np.copy(alphaG) - i = 0 - K_s = np.zeros(niter) - tg=1 - - - #Beginning of main loop - while i < niter: - print('main loop: ',i) - - DS = Y-G - - ts = 1 - for j in range(riter): - # S = tools.Forward_Backward(DS, S, FS_op, IS_op, muS, regS0) - alphaS, csiS, ts = tools.FISTA(DS, alphaS, FS_op, IS_op, muS, ts, csiS, regS1, transform, inverse, pos = 1) - - S = inverse(alphaS)#*supp - S[S<0] = 0 - FS = FS_op(S) - - - - DG = Y-FS - for j2 in range(riter): - alphaG, csiG, tg = tools.FISTA(DG, alphaG, FG_op, IG_op, muG, tg, csiG, regG1, transform, inverse, pos = 1) - #Image to approximate by solving the problem in G - G = inverse(alphaG) - - # - newres = (np.std(Y-FS-G)**2)/sigma0**2 - K_s[i] = newres - res = np.copy(newres) - - plt.figure(0) - plt.subplot(221) - plt.title('S') - plt.imshow(S) - plt.subplot(222) - plt.title('FS') - plt.imshow(FS) - plt.subplot(223) - plt.title('G') - plt.imshow(G) - plt.subplot(224) - plt.title('Residuals') - plt.imshow(Y-FS-G) - plt.savefig('Res'+str(i)+'.png') - i +=1 - #Weighting - - weightS = 1./(1.+np.exp(-10.*(levels*kmax*sigma0-alphaS))) - weightG = 1./(1.+np.exp(-10.*(levelg*kmax*sigma0-alphaG))) - - - S, FS = SLIT(Y-G, Fkappa, kmax, niter, size, PSF, PSFconj, S0 = S, levels = levels, mask = mask, lvl = lvls) - - #Final reconstructions - plt.show() - plt.plot(K_s); plt.show() - return S, FS,G - - - - - - -################################### TOOLS ################################### - -def MOM(Y, levels, levelg, kmax, transform, inverse, IS_op, sigma, niter, I = 0): - - Gw0 = transform((Y))[:-1,:,:] - levelg1 = levelg[:-1,:,:] - Gw = Gw0[levelg1!=0]/levelg[levelg1!=0]/sigma - kG = np.max(Gw) - kG0 = kG - stepG = (kG-kmax)/(niter-I-5) - - - FS0 = Y - Sw0 = transform(IS_op(FS0))[:-1,:,:] - levels1 = levels[:-1,:,:] - Sw = Sw0[levels1!=0]/levels[levels1!=0]/sigma - kS = np.max(Sw) - - k =np.min([kG,kS]) - k = np.max([k,kmax])+(np.abs(kS-kG))/100. - step = (k-kmax)/(niter-I-5) - return k, step - -def plot_cube(cube): - ##DESCRIPTION: - ## Plotting device that displays layers of a cube in different subplot panels. - ## - ##INPUTS: - ## -cube: Cube for which to plot the layers with shape (n,n1,n2) with n, the number of layers and n1xn2, the number of pixels. - ## - ##OUTPUTS: - ## -None - n,n1,n2 = np.shape(cube) - i = n/2 - if i == n/2.+0.5: - i+=1 - j = 2 - for k in range(n): - plt.subplot(i,j,k) - plt.imshow(cube[k,:,:]); plt.colorbar() - - return None - - -def level(n1,n2, lvl): - ##DESCRIPTION: - ## Estimates the noise levels in starlet space in image plane. - ## - ##INPUTS: - ## -n1,n2: shape of the image for which to get noise levels - ## - ##OUTPUTS: - ## -levels: units of noise levels at each scale and location of a starlet transform - dirac = np.zeros((n1,n2)) - # lvl = np.int(np.log2(n1)) - dirac[n1/2,n2/2] = 1 - wave_dirac = mw.wave_transform(dirac,lvl, newwave = 0) - - wave_sum = np.sqrt(np.sum(np.sum(wave_dirac**2,1),1)) - levels = np.multiply(np.ones((lvl,n1,n2)).T,wave_sum).T - - return levels - -def level_source(n1,n2,sigma,size,PSFT, Lens_op2, lensed, lvl): - ns1,ns2 = n1*size, n2*size - ones = np.ones((n1,n2)) - lensed[lensed == 0] = 1 - noise = ones*sigma - Hnoise = noise*np.sqrt(np.sum(PSFT**2))#np.sqrt(scp.fftconvolve(noise**2, PSFT**2, mode = 'same'))## - FHnoise = Lens_op2(Hnoise) - FHnoise[FHnoise==0] = np.mean(FHnoise)*10. - dirac = np.zeros((ns1,ns2)) - dirac[ns1/2,ns2/2] = 1 - wave_dirac = mw.wave_transform(dirac, lvl) - levels = np.zeros(wave_dirac.shape) - for i in range(lvl): - if np.size(noise.shape) > 2: - lvlso = (scp.fftconvolve(FHnoise[i, :, :] ** 2, wave_dirac[i, :, :] ** 2, - mode='same')) - else: - lvlso = scp.fftconvolve(FHnoise ** 2, wave_dirac[i,:,:] ** 2, - mode='same') - levels[i, :, :] = np.sqrt(np.abs(lvlso)) - - return levels - -def spectralNorm(nx,ny,Niter,tol,f,finv): - ##DESCRIPTION: - ## Function that estimates the source light profile from an image of a lensed source given the mass density profile. - ## - ##INPUTS: - ## -nx,ny: shape of the input - ## -nz: number of decomposition scales (if the operator tis a multiscale decomposition for instance) - ## -Niter: number of iterations - ## -tol: tolerance error as a stopping criteria - ## -f: operator - ## -finv: inverse operator - ## - ##OUTPUTS: - ## -SspNorm: The spectral norm of the operator - - #### Initilize array with random numbers ### - matA = np.random.randn(nx,ny) - ### Normalize the input ### - spNorm = LA.norm(matA) - matA /= spNorm - matA = np.array(matA) - it = 0 - err = abs(tol) - while it < Niter and err >= tol: - ### Apply operator ### - wt = f(matA) - ### Apply joint operator ### - matA = finv(wt) - ### Compute norm ### - spNorm_new = LA.norm(matA) - matA /= spNorm_new - err = abs(spNorm_new - spNorm)/spNorm_new - spNorm = spNorm_new - it += 1 - return spNorm - - - -def lens_one(Fkappa, n1,n2,size): - ##DESCRIPTION: - ## Function that maps an all at one image to source plane. - ## - ##INPUTS: - ## -Fkappa: the mapping between source and image planes - ## -n1,n2: the shape of the image. - ## -size: the factor that scales the shape of the source relative to the shape of the image - ## - ##OUTPUTS: - ## -lensed: the projection to source plane of an all at aone image. - dirac = np.ones((n1,n2)) - lensed = Lens.image_to_source(dirac, size,Fkappa,lensed = [0]) - return lensed - -def mk_bound(Fkappa, n1,n2,size): - ##DESCRIPTION: - ## Function that returns the support of the lens image in source plane. - ## - ##INPUTS: - ## -Fkappa: the mapping between source and image planes - ## -n1,n2: the shape of the image. - ## -size: the factor that scales the shape of the source relative to the shape of the image - ## - ##OUTPUTS: - ## -lensed: the projection to source plane of an all at aone image. - dirac = np.ones((n1,n2)) - lensed = Lens.image_to_source_bound(dirac, size,Fkappa,lensed = [0]) - bound = lensed/lensed - bound[lensed==0]=0 - return bound - - -def MAD(x,n=3): - ##DESCRIPTION: - ## Estimates the noise standard deviation from Median Absolute Deviation - ## - ##INPUTS: - ## -x: a 2D image for which we look for the noise levels. - ## - ##OPTIONS: - ## -n: size of the median filter. Default is 3. - ## - ##OUTPUTS: - ## -S: the source light profile. - ## -FS: the lensed version of the estimated source light profile - x = mw.wave_transform(x, np.int(np.log2(x.shape[0])))[0,:,:] - meda = med.median_filter(x,size = (n,n)) - medfil = np.abs(x-meda) - sh = np.shape(x) - sigma = 1.48*np.median((medfil)) - return sigma - -def MAD_poisson(x,tau,n=3): - ##DESCRIPTION: - ## Estimates the noise standard deviation from Median Absolute Deviation - ## - ##INPUTS: - ## -x: a 2D image for which we look for the noise levels. - ## - ##OPTIONS: - ## -n: size of the median filter. Default is 3. - ## - ##OUTPUTS: - ## -S: the source light profile. - ## -FS: the lensed version of the estimated source light profile - n1,n2 = np.shape(x) - lvl = np.int(np.log2(x.shape[0]))-1 - new_x, y = wine.MCA.mr_filter(x,20,8,MAD(x), lvl = lvl) - plt.imshow(new_x); plt.show() - sigma = np.sqrt(np.abs(new_x)/tau) - return sigma - - - -def ST(alpha, k, levels, sigma, hard = 0): - ##DESCRIPTION: - ## Soft thresholding operator. - ## - ##INPUTS: - ## -alpha: the starlet decomposition to be thresholded. - ## -k: the threshold in units of noise levels (usually 5). - ## -levels: the noise levels at each scale and location of the starlet decomposition. - ## -sigma: the noise standard deviation. - ## - ##OUTPUTS: - ## -alpha: The thresholded coefficients. - lvl, n1,n2 = np.shape(alpha) - th = np.ones((lvl,n1,n2))*k - th[0,:,:] = th[0,:,:]+3 - th[-1,:,:] = 0 - - - alpha0 = np.copy(alpha) - th = th*levels*sigma - - if hard == 0: - alpha= np.sign(alpha0)*(np.abs(alpha0)-th) - alpha[np.where(np.abs(alpha)-th<0)]=0 - - - return alpha - - -def mk_simu(n1,n2,lvl,size, sigma, I_op, transform, n): - storage = np.zeros((lvl,n1*size, n2*size, n)) - for i in range(n): - noise = np.random.randn(n1,n2)*sigma - noise_lens = I_op(noise) - noise_lens[noise_lens ==0] = 1 - storage[:,:,:,i] = transform(noise_lens) - return storage - - -def simulate_noise(n1,n2, sigma, size, I_op, transform, lvl, Npar = np.int(mtp.cpu_count()/2)): - ##DESCRIPTION: - ## Simulates noise levels in source plane from lensing operator and convolution operator. - ## - ##INPUTS: - ## -n1,n2: the shape of the images for which to simulate noise maps. - ## -size: scaling factor for the shape of the source. - ## -Fkappa: Projection operator between lens and source plane. - ## -lensed: mapping of an all at one image to source plane. - ## -PSFconj: the conjugate of the PSF - ## - ##OPTIONS: - ## -n: size of the median filter. Default is 3. - ## - ##OUTPUTS: - ## -S: the source light profile. - ## -FS: the lensed version of the estimated source light profile - n = 500 - if Npar>mtp.cpu_count(): - Npar = mtp.cpu_count() - ns1,ns2 = n1*size, n2*size -# lvl = np.int(np.log2(ns1)) - w_levels = np.zeros((lvl,ns1,ns2)) - - p = Pool(Npar) - storage = mk_simu(n1,n2,lvl,size, sigma, I_op, transform,n) - - w_levels = np.std(storage, axis = 3) -# w_levels[0,:,:] = w_levels[0,:,:]*6/5 - - return w_levels - - - - diff --git a/build/lib/SLIT/__init__.py b/build/lib/SLIT/__init__.py deleted file mode 100644 index a7d6663..0000000 --- a/build/lib/SLIT/__init__.py +++ /dev/null @@ -1,4 +0,0 @@ -from Solve import * -import Lens -import wave_transform -import tools diff --git a/build/lib/SLIT/tools.py b/build/lib/SLIT/tools.py deleted file mode 100644 index 546727d..0000000 --- a/build/lib/SLIT/tools.py +++ /dev/null @@ -1,255 +0,0 @@ -import numpy as np -import matplotlib.pyplot as plt -import pyfits as pf -import scipy.ndimage.filters as sc -import scipy.ndimage.filters as med -import scipy.signal as cp - -def MAD(x,n=3): - ##DESCRIPTION: - ## Estimates the noise standard deviation from Median Absolute Deviation - ## - ##INPUTS: - ## -x: a 2D image for which we look for the noise levels. - ## - ##OPTIONS: - ## -n: size of the median filter. Default is 3. - ## - ##OUTPUTS: - ## -S: the source light profile. - ## -FS: the lensed version of the estimated source light profile - x = wave_transform(x, np.int(np.log2(x.shape[0])))[0,:,:] - meda = med.median_filter(x,size = (n,n)) - medfil = np.abs(x-meda) - sh = np.shape(x) - sigma = 1.48*np.median((medfil)) - return sigma - -def Forward_Backward(Y, X, F_op, I_op, mu, reg, pos = 1): - - R = mu*I_op(Y-F_op(X)) - Xnew = np.copy(X+R) - Xnew, M = reg(Xnew) - if pos == 1: - Xnew[Xnew<0] = 0 - return Xnew, M - -def Primal_dual(Y, X, U, mu, nu, tau, F_op, I_op, transform, inverse, reg): - p = X+mu*I_op(Y-F_op(X))-mu*inverse(U) - # plot_cube(U+nu*transform(2*p-X)); plt.show() - q = reg(U+nu*transform(2*p-X)) - X =tau*p+(1-tau)*X - U =tau*q+(1-tau)*U -# plot_cube(q); plt.show() - return X,U - - -def FISTA(Y, alphaX, F_op, I_op, mu, ts, csi, reg, transform, inverse, pos = 1, mask = 1): - S = inverse(alphaX) - #S[S>size*np.max(Y)] = np.max(Y) - # S[S<0] = 0 - R = mu*I_op(Y-F_op(S)*mask) - alpha = transform(R)+csi - alpha, M = reg(alpha) - tsnew = (1.+np.sqrt(1.+4.*ts**2))/2. - csi = alpha+((ts-1)/tsnew)*(alpha-alphaX) - return alpha, csi, tsnew - -def Soft(X, transform, inverse, level, k, supp =1): - Xnew = np.sign(X)*(np.abs(X)-level*k) - Xnew[np.where((np.abs(X)-level*k)<0)] = 0 - - Xnew[-1,:,:] = X[-1,:,:] - - #print(Xnew.shape, supp.shape) - Xnew = Xnew*supp - return Xnew - -def Soft_Threshold(X, transform, inverse, level, k, supp =1): - X = transform(X) - alpha = wave_transform(X,Xw.shape[0],newwave = 0) - M = np.zeros(alpha.shape) - M[np.abs(alpha)-level*k>0] = 1 - M[0,:,:] = 0 - M[0,np.abs(alpha[0,:,:]) - level[0,:,:] * (k+1) > 0] = 1 - - Xnew = np.sign(X)*(np.abs(X)-level*k) - Xnew = Xnew*M - Xnew[-1,:,:] = X[-1,:,:] - Xnew = Xnew*supp - return inverse(Xnew), M - -def Hard(X, transform, inverse, level, k, supp=1): - Xnew = np.copy(X) - Xnew[np.where((np.abs(X)-level*k)<0)] = 0 - - Xnew[-1,:,:] = X[-1,:,:] - Xnew = Xnew*supp -## plt.figure(0) -## plot_cube(X) -## plt.figure(1) -## plot_cube(Xnew) -## plt.show() - return Xnew, M - -def Hard_Threshold(X, transform, inverse, level, k, supp=1): - Xw = transform(X) - alpha = wave_transform(X,Xw.shape[0],newwave = 0) - M = np.zeros(alpha.shape) - M[np.abs(alpha)-level*k>0] = 1 - M[0,:,:] = 0 - M[0,np.abs(alpha[0,:,:]) - level[0,:,:] * (k+1) > 0] = 1 - - Xnew=M*Xw - Xnew[-1,:,:] = Xw[-1,:,:] - Xnew = Xnew*supp - return inverse(Xnew), M - -def mr_filter(Y, level, k, niter, transform, inverse, lvl = 6, Soft = 0, pos = 1): - Xnew = 0 - alpha = wave_transform(Y, lvl, newwave=0) - M = np.zeros(alpha.shape) - M[np.abs(alpha)-level*k>0] = 1 - M[0,:,:] = 0 - M[0,np.abs(alpha[0,:,:]) - level[0,:,:] * (k+1) > 0] = 1 - M[-1,:,:] =1 - i=0 - while i < niter: - R = Y-Xnew - - if Soft == True : - Rnew= Soft_threshold(R, transform, inverse, level,k) - else: - - Rnew = Hard_Threshold(R, transform, inverse, level,k) - # Rnew = inverse(transform(R)*M) - Xnew = Xnew+Rnew - - if pos == True: - Xnew[Xnew < 0] = 0 - - i = i+1 - - return (Xnew), M - -def wave_transform(img, lvl, Filter = 'Bspline', newwave = 1, convol2d = 0): - - mode = 'nearest' - - lvl = lvl-1 - sh = np.shape(img) - if np.size(sh) ==3: - mn = np.min(sh) - wave = np.zeros([lvl+1,sh[1], sh[1],mn]) - for h in np.linspace(0,mn-1, mn): - if mn == sh[0]: - wave[:,:,:,h] = wave_transform(img[h,:,:],lvl+1, Filter = Filter) - else: - wave[:,:,:,h] = wave_transform(img[:,:,h],lvl+1, Filter = Filter) - return wave - n1 = sh[1] - n2 = sh[1] - - if Filter == 'Bspline': - h = [1./16, 1./4, 3./8, 1./4, 1./16] - else: - h = [1./4,1./2,1./4] - n = np.size(h) - h = np.array(h) - - if n+2**(lvl-1)*(n-1) >= np.min([n1,n2])/2.: - lvl = np.int_(np.log2((n1-1)/(n-1.))+1) - - c = img - ## wavelet set of coefficients. - wave = np.zeros([lvl+1,n1,n2]) - - for i in np.linspace(0,lvl-1,lvl): - newh = np.zeros((1,n+(n-1)*(2**i-1))) - newh[0,np.int_(np.linspace(0,np.size(newh)-1,len(h)))] = h - H = np.dot(newh.T,newh) - - ######Calculates c(j+1) - ###### Line convolution - if convol2d == 1: - cnew = cp.convolve2d(c, H, mode='same', boundary='symm') - else: - cnew = sc.convolve1d(c,newh[0,:],axis = 0, mode =mode) - - ###### Column convolution - cnew = sc.convolve1d(cnew,newh[0,:],axis = 1, mode =mode) - - - - if newwave ==1: - ###### hoh for g; Column convolution - if convol2d == 1: - hc = cp.convolve2d(cnew, H, mode='same', boundary='symm') - else: - hc = sc.convolve1d(cnew,newh[0,:],axis = 0, mode = mode) - - ###### hoh for g; Line convolution - hc = sc.convolve1d(hc,newh[0,:],axis = 1, mode = mode) - - ###### wj+1 = cj-hcj+1 - wave[i,:,:] = c-hc - - else: - ###### wj+1 = cj-cj+1 - wave[i,:,:] = c-cnew - - - c = cnew - - wave[i+1,:,:] = c - - return wave - -def iuwt(wave, convol2d =0): - mode = 'nearest' - - lvl,n1,n2 = np.shape(wave) - h = np.array([1./16, 1./4, 3./8, 1./4, 1./16]) - n = np.size(h) - - cJ = np.copy(wave[lvl-1,:,:]) - - - for i in np.linspace(1,lvl-1,lvl-1): - - newh = np.zeros((1,n+(n-1)*(2**(lvl-1-i)-1))) - newh[0,np.int_(np.linspace(0,np.size(newh)-1,len(h)))] = h - H = np.dot(newh.T,newh) - - ###### Line convolution - if convol2d == 1: - cnew = cp.convolve2d(cJ, H, mode='same', boundary='symm') - else: - cnew = sc.convolve1d(cJ,newh[0,:],axis = 0, mode = mode) - ###### Column convolution - cnew = sc.convolve1d(cnew,newh[0,:],axis = 1, mode = mode) - - cJ = cnew+wave[lvl-1-i,:,:] - - return np.reshape(cJ,(n1,n2)) - - -def plot_cube(cube): - ##DESCRIPTION: - ## Plotting device that displays layers of a cube in different subplot panels. - ## - ##INPUTS: - ## -cube: Cube for which to plot the layers with shape (n,n1,n2) with n, the number of layers and n1xn2, the number of pixels. - ## - ##OUTPUTS: - ## -None - n,n1,n2 = np.shape(cube) - i = n/2 - if i == n/2.+0.5: - i+=1 - j = 2 - for k in range(n): - plt.subplot(i,j,k) - plt.imshow(cube[k,:,:]); plt.colorbar() - - return None diff --git a/build/lib/SLIT/wave_transform.py b/build/lib/SLIT/wave_transform.py deleted file mode 100644 index ed28a82..0000000 --- a/build/lib/SLIT/wave_transform.py +++ /dev/null @@ -1,141 +0,0 @@ -import numpy as np -import scipy.signal as cp -import matplotlib.pyplot as plt -import scipy.ndimage.filters as sc - - -def symmetrise(img, size): - - n3, n4 = np.shape(img) - n1,n2 = size - img[:(n3-n1)/2, :] = np.flipud(img[(n3-n1)/2:(n3-n1),:]) - img[:,:(n4-n2)/2] = np.fliplr(img[:,(n4-n2)/2:(n4-n2)]) - img[(n3+n1)/2:,:] = np.flipud(img[n1:(n3+n1)/2,:]) - img[:,(n4+n2)/2:] = np.fliplr(img[:,n2:(n4+n2)/2]) - - return img - - -def fft_convolve(X,Y, inv = 0): - - XF = np.fft.rfft2(X) - YF = np.fft.rfft2(Y) -# YF0 = np.copy(YF) -# YF.imag = 0 -# XF.imag = 0 - if inv == 1: - # plt.imshow(np.real(YF)); plt.colorbar(); plt.show() - YF = np.conj(YF) - - SF = XF*YF - - S = np.fft.irfft2(SF) - n1,n2 = np.shape(S) - - S = np.roll(S,-n1/2+1,axis = 0) - S = np.roll(S,-n2/2+1,axis = 1) - - return np.real(S) - - -def wave_transform(img, lvl, Filter = 'Bspline', newwave = 1, convol2d = 0): - - mode = 'nearest' - - lvl = lvl-1 - sh = np.shape(img) - if np.size(sh) ==3: - mn = np.min(sh) - wave = np.zeros([lvl+1,sh[1], sh[1],mn]) - for h in np.linspace(0,mn-1, mn): - if mn == sh[0]: - wave[:,:,:,h] = wave_transform(img[h,:,:],lvl+1, Filter = Filter) - else: - wave[:,:,:,h] = wave_transform(img[:,:,h],lvl+1, Filter = Filter) - return wave - n1 = sh[1] - n2 = sh[1] - - if Filter == 'Bspline': - h = [1./16, 1./4, 3./8, 1./4, 1./16] - else: - h = [1./4,1./2,1./4] - n = np.size(h) - h = np.array(h) - - if n+2**(lvl-1)*(n-1) >= np.min([n1,n2])/2.: - lvl = np.int_(np.log2((n1-1)/(n-1.))+1) - - c = img - ## wavelet set of coefficients. - wave = np.zeros([lvl+1,n1,n2]) - - for i in np.linspace(0,lvl-1,lvl): - newh = np.zeros((1,n+(n-1)*(2**i-1))) - newh[0,np.int_(np.linspace(0,np.size(newh)-1,len(h)))] = h - H = np.dot(newh.T,newh) - - ######Calculates c(j+1) - ###### Line convolution - if convol2d == 1: - cnew = cp.convolve2d(c, H, mode='same', boundary='symm') - else: - cnew = sc.convolve1d(c,newh[0,:],axis = 0, mode =mode) - - ###### Column convolution - cnew = sc.convolve1d(cnew,newh[0,:],axis = 1, mode =mode) - - - - if newwave ==1: - ###### hoh for g; Column convolution - if convol2d == 1: - hc = cp.convolve2d(cnew, H, mode='same', boundary='symm') - else: - hc = sc.convolve1d(cnew,newh[0,:],axis = 0, mode = mode) - - ###### hoh for g; Line convolution - hc = sc.convolve1d(hc,newh[0,:],axis = 1, mode = mode) - - ###### wj+1 = cj-hcj+1 - wave[i,:,:] = c-hc - - else: - ###### wj+1 = cj-cj+1 - wave[i,:,:] = c-cnew - - - c = cnew - - wave[i+1,:,:] = c - - return wave - -def iuwt(wave, convol2d =0): - mode = 'nearest' - - lvl,n1,n2 = np.shape(wave) - h = np.array([1./16, 1./4, 3./8, 1./4, 1./16]) - n = np.size(h) - - cJ = np.copy(wave[lvl-1,:,:]) - - - for i in np.linspace(1,lvl-1,lvl-1): - - newh = np.zeros((1,n+(n-1)*(2**(lvl-1-i)-1))) - newh[0,np.int_(np.linspace(0,np.size(newh)-1,len(h)))] = h - H = np.dot(newh.T,newh) - - ###### Line convolution - if convol2d == 1: - cnew = cp.convolve2d(cJ, H, mode='same', boundary='symm') - else: - cnew = sc.convolve1d(cJ,newh[0,:],axis = 0, mode = mode) - ###### Column convolution - cnew = sc.convolve1d(cnew,newh[0,:],axis = 1, mode = mode) - - cJ = cnew+wave[lvl-1-i,:,:] - - return np.reshape(cJ,(n1,n2)) - diff --git a/dist/SLIT-0.1-py2.7.egg b/dist/SLIT-0.1-py2.7.egg deleted file mode 100644 index 6ff418b..0000000 Binary files a/dist/SLIT-0.1-py2.7.egg and /dev/null differ diff --git a/setup.py b/setup.py index 031def3..ec3257d 100644 --- a/setup.py +++ b/setup.py @@ -1,9 +1,20 @@ -from setuptools import setup - -setup(name='SLIT', - version='0.1', - description='Code for colour lens/source separation and lensed source reconstruction', - author='Remy Joseph, Frederic Courbin, Jean-Luc Starck', - author_email='remy.joseph@epfl.ch', - packages=['SLIT'], - zip_safe=False) +import os +import sys +from setuptools import find_packages + +try: + from setuptools import setup +except ImportError: + from distutils.core import setup + +PACKAGE_PATH = os.path.abspath(os.path.join(__file__, os.pardir)) + +setup(name='SLIT', + version='0.1', + description='Code for colour lens/source separation and lensed source reconstruction', + author='Remy Joseph, Frederic Courbin, Jean-Luc Starck', + author_email='remy.joseph@epfl.ch', + # packages=['SLIT'], + packages=find_packages(PACKAGE_PATH), + zip_safe=False, +)