README.md

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.

What's New (v0.1.13)

• Changes in supported types in denoise and denoiseall functions. For the inputtype positional argument, the initially supported arguments :acwt and :acwpt are now changed to :acdwt and :acwpd to match the function name change in WaveletsExt.ACWT.
• 2D Local Discriminant Basis now supported. 2D version of LDB is now up and running without any changes in the syntax compared to the 1D version.

What's New (v0.1.12)

• Bug fixes on best basis algorithms to allow compatibility when partial wavelet decomposition is run.
• New function plot_tfbdry2() implemented. Visual representation of leaf nodes for 2D best basis trees now available.

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):

• Inverse Transforms for Shift-Invariant WPT
• nD wavelet transforms for redundant and non-redundant versions