WaveletsExt.jl

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This package is a Julia extension package to Wavelets.jl (WaveletsExt is short for Wavelets Extension). It contains additional functionalities that complement Wavelets.jl, namely

• Multi-dimensional wavelet transforms
• Redundant wavelet transforms
  • Autocorrelation Wavelet Transforms (ACWT)
  • Stationary Wavelet Transforms (SWT)
  • Shift Invariant Wavelet Transforms (SIWT)
• Best basis algorithms
  • Joint best basis (JBB)
  • Least statistically dependent basis (LSDB)
• Denoising methods
  • Relative Error Shrink (RelErrorShrink)
  • Stein Unbiased Risk Estimator Shrink (SUREShrink)
• Wavelet transform based feature extraction techniques
  • Local Discriminant Basis (LDB)

Authors

This package is written and maintained by Zeng Fung Liew and Shozen Dan under the supervision of Professor Naoki Saito at the University of California, Davis.

Installation

The package is part of the official Julia Registry. It can be install via the Julia REPL.

(@1.7) pkg> add WaveletsExt

or

julia> using Pkg; Pkg.add("WaveletsExt")

Usage

Load the WaveletsExt module along with Wavelets.jl.

using Wavelets, WaveletsExt

References

[1] Coifman, R.R., Wickerhauser, M.V. (1992). Entropy-based algorithms for best basis selection. DOI: 10.1109/18.119732
[2] Saito, N. (1998). The least statistically-dependent basis and its applications. DOI: 10.1109/ACSSC.1998.750958
[3] Beylkin, G., Saito, N. (1992). Wavelets, their autocorrelation functions, and multiresolution representations of signals. DOI: 10.1117/12.131585
[4] Nason, G.P., Silverman, B.W. (1995) The Stationary Wavelet Transform and some Statistical Applications. DOI: 10.1007/978-1-4612-2544-7_17
[5] Donoho, D.L., Johnstone, I.M. (1995). Adapting to Unknown Smoothness via Wavelet Shrinkage. DOI: 10.1080/01621459.1995.10476626
[6] Saito, N., Coifman, R.R. (1994). Local Discriminant Basis. DOI: 10.1117/12.188763
[7] Saito, N., Coifman, R.R. (1995). Local discriminant basis and their applications. DOI: 10.1007/BF01250288
[8] Saito, N., Marchand, B. (2012). Earth Mover's Distance-Based Local Discriminant Basis. DOI: 10.1007/978-1-4614-4145-8_12
[9] Cohen, I., Raz, S., Malah, D. (1997). Orthonormal shift-invariant wavelet packet decomposition and representation. DOI: 10.1016/S0165-1684(97)00007-8
[10] Irion, J., Saito, N. (2017). Efficient Approximation and Denoising of Graph Signals Using the Multiscale Basis Dictionaries. DOI: 10.1109/TSIPN.2016.2632039

TODO(long term):

• nD wavelet transforms for redundant and non-redundant versions