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This document is intended to serve as an introduction to Wavelet processing through a set of Matlab experiments. These experiments will gives an overview of three fundamental tasks in signal and image processing : approximation, denoising and compression. These scripts are self contented (needed additional Matlab functions can be downloaded while reading the lectures).
The main reference for an indepth explanation of Wavelet processing is
A Wavelet Tour of Signal Processing
Stéphane Mallat, Academic Press; 2 edition (September 15, 1999)Each one of these five lectures should take between 1h and 2h in order to test the various features of the scripts. One should copy/paste the provided code into a file named e.g. tp1.m, and launch the script directly from Matlab comand line > tp1;. Some of the scripts contain "holes" that you should try to fill on your own.
I also provide the complete correction of these lectures as a set of Matlab scripts, but you should try as much as possible to avoid using them.
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Basic Matlab instructions. | |
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Linear and non-linear wavelet approximation of signals. | |
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Linear and non-linear wavelet approximation of images. | |
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Denoising using filtering. | |
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Denoising using wavelet thresholding. | |
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Wavelet compression of 1D signals. | |
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Image Compression. |
Copyright © 2006 Gabriel Peyré