lanicon/sharpwave

A refactored port and code rebuilt of JWave - Discrete Fourier Transform (DFT), Fast Wavelet Transform (FWT), Wavelet Packet Transform (WPT), some Shifting Wavelet Transform (SWT) by using orthogonal (orthonormal) wavelets like Haar, Daubechie, Coiflet, and other normalized bi-orthogonal wavelets.

sharpWave

A refactored port of JWave to C#

Introduction

JWave was ported to sharpWave using Microsoft's C# programming language.

HowTo

For some how to use it; JWave's github.io

building

For having a quick example, use GNU/Linux having the mono compiler available. Then try:

git clone https://github.com/graetz23/sharpWave.git && cd sharpWave && make run

remarks

The following functionality is available:

• The 1-D, 2-D, and 3-D orthogonal transform algorithms; class Algorithm:
  • a kind of Fast Wavelet Transform (FWT); class FastWaveletTransform,
  • a (Fast) Wavelet Packet Transform (WPT); class WaveletPacketTransform,
  • some Shifting Wavelet Transform (SWT); class ShiftingWaveletTransform,
  • and a Discrete Fourier Transform (DFT); class DiscreteFourierTransform.
• Orthogonal and in most cases orthonormal wavelets:
  • Orthonormal Alfred Haar's Wavelet; class Haar1,
  • Orthogonal Alfred Haar's Wavelet; class Haar1Orthogonal,
  • Orthonormal Coiflet wavelet family; file Coiflet.cs:
    • Coiflet 1 wavelet,
    • Coiflet 2 wavelet; reconstrucion error ~1e-10,
    • Coiflet 3 wavelet; reconstrucion error ~1e-12,
    • Coiflet 4 wavelet; reconstrucion error ~1e-10,
    • Coiflet 5 wavelet; reconstrucion error ~1e-08.
  • Orthonormal Legendre wavelet family; file Legendre.cs:
    • Legendre 1 wavelet,
    • Legendre 2 wavelet; not working properly,
    • Legendre 3 wavelet; not working properly.
  • Ingrid Daubechies' orthonormal wavelet family; file Daubechies.cs:
    • Daubechies 2 wavelet,
    • Daubechies 3 wavelet,
    • Daubechies 4 wavelet; reconstrucion error ~1e-12,
    • Daubechies 5 wavelet; reconstrucion error ~1e-12,
    • Daubechies 6 wavelet; reconstrucion error ~1e-12,
    • Daubechies 7 wavelet; reconstrucion error ~1e-12,
    • Daubechies 8 wavelet; reconstrucion error ~1e-12,
    • Daubechies 9 wavelet; reconstrucion error ~1e-10,
    • Daubechies 10 wavelet; reconstrucion error ~1e-10,
    • Daubechies 11 wavelet; reconstrucion error ~1e-12,
    • Daubechies 12 wavelet; reconstrucion error ~1e-14.
  • Orthonormal Symlet wavelet family; file Symlet.cs:
    • Symlet 2 wavelet,
    • Symlet 3 wavelet: reconstrucion error ~1e-10,
    • Symlet 4 wavelet: reconstrucion error ~1e-10,
    • Symlet 5 wavelet: reconstrucion error ~1e-12,
    • Symlet 6 wavelet: reconstrucion error ~1e-10,
    • Symlet 7 wavelet: reconstrucion error ~1e-10,
    • Symlet 8 wavelet: reconstrucion error ~1e-12,
    • Symlet 9 wavelet: reconstrucion error ~1e-12,
    • Symlet 10 wavelet: reconstrucion error ~1e-14,
    • Symlet 11 wavelet: reconstrucion error ~1e-14,
    • Symlet 12 wavelet: reconstrucion error ~1e-14,
  • Cohen Daubechies Feauveau orthogonal wavelet family; file CDF.cs:
    • Cohen Daubechies Feauveau (CDF) 5/3; not working properly,
    • Cohen Daubechies Feauveau (CDF) 9/7; not working properly.
  • Orthogonal Mallat's Battle 23; class Battle23; not working properly,
  • Orthogonal Discrete Mayer Wavelet; class DiscreteMayer; strong reconstrucion error; ~1e-2.
• Everything was coded using:
  • atom editor,
  • mono compiler,
  • Gnome windows manager,
  • and debian GNU/Linux,

have fun :-)

ChangeLog

20200320

• grouping all Coiflet wavelets in file: Coiflet.cs,
• grouping all Daubechies wavelets in file: Daubechies.cs,
• grouping all Legendre wavelets in file: Legendre.cs,
• grouping all CDF wavelets in file: CDF.cs,
• added the Symlet 3 wavelet,
• added the Symlet 4 wavelet,
• added the Symlet 5 wavelet,
• added the Symlet 6 wavelet,
• added the Symlet 7 wavelet,
• added the Symlet 8 wavelet,
• added the Symlet 9 wavelet,
• added the Symlet 10 wavelet,
• added the Symlet 11 wavelet,
• added the Symlet 12 wavelet.

20200319

• added the Daubechies 3 wavelet,
• added the Daubechies 4 wavelet,
• added the Daubechies 5 wavelet,
• added the Daubechies 6 wavelet,
• added the Daubechies 7 wavelet,
• added the Daubechies 8 wavelet,
• added the Daubechies 9 wavelet,
• added the Daubechies 10 wavelet,
• added the Daubechies 11 wavelet,
• added the Daubechies 12 wavelet.

20200318

• added the Coiflet 2 wavelet,
• added the Coiflet 3 wavelet,
• added the Coiflet 4 wavelet,
• added the Coiflet 5 wavelet,
• added the Mallat's Battle 23 wavelet,
• added the Cohen Daubechies Feauveau (CDF) 5/3 wavelet,
• added the Cohen Daubechies Feauveau (CDF) 9/7 wavelet.

20200317

• renamed class BasicTransform to Algorithm,
• ported Alfred Haar's orthogonal wavelet:
  • extended the explanation of orthogonality and orthonormality,
  • made the methods forward and reverse of class Wavelet virtual.
• added the Coiflet 1 wavelet,
• added the Legendre 1 wavelet,
• added the Legendre 2 wavelet,
• added the Legendre 3 wavelet,
• added the Daubechies 2 wavelet,
• added the Symlet 2 wavelet.
• added the DiscreteMayer wavelet.

20200316

• ported the Discrete Fourier Transform (DFT),
• ported the some Shifting Wavelet Transform (SWT),
• ported the (Fast) Wavelet Packet Transform (WPT); Wavelet Packet Decomposition (WPD),
• extended the class SharpWave for testing the SWT algorithm.
• extended the class SharpWave for testing the WPT / WPD algorithm.

20200315

• ported getter methods to C#'s lambda style
• reconstructed the Constructors of Transform classes,
• decided to use C#'s multidimensional instead of jagged arrays,
• added 2-D forward and reverse (stepping) algorithms,
• added 3-D forward and reverse (stepping) algorithms,
• extended the main method by 2-D example,
• recycled comments towards C#'s XML style,
• cleaned code.

20200314

• added 1-D orthogonal transform functions,
• added the Fast Wavelet Transform algorithms,
• added the orthonormal Haar Wavelet.

20200304

• started the ported,
• ported all necessary classes for a minimal example.