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The Wavelet Transform

Introduction

The continuous wavelet transform

Examples of Wavelets

Morlet's Wavelet

Mexican Hat

The discrete wavelet transform

Introduction

Multiresolution Analysis

The à trous algorithm

Pyramidal Algorithm

The Laplacian Pyramid

Pyramidal Algorithm with one Wavelet

Multiresolution with scaling functions with a frequency
cut-off

The Wavelet transform using the Fourier transform

The Reconstruction

Visualization of the Wavelet Transform

Visualisation of the first class

Visualisation of the second class

Visualisation of the third class

Noise reduction from the wavelet transform

The convolution from the continuous wavelet transform

The Wiener-like filtering in the wavelet space

Hierarchical Wiener filtering

Adaptive filtering from the wavelet transform

Hierarchical adaptive filtering

Comparison using a multiresolution quality criterion

Deconvolution

Introduction

Regularization in the wavelet space

Tikhonov's regularization and multiresolution analysis

Regularization from significant structures

Regularization of Van Cittert's algorithm

Regularization of the one-step gradient method

Regularization of Lucy's algorithm

Convergence

The wavelet context in MIDAS

Introduction

Commands Description

TRANSF/WAVE

RECONS/WAVE

HEADER/WAVE

INFO/WAVE

EXTRAC/WAVE

ENTER/WAVE

VISUAL/WAVE

VISUAL/CUB

VISUAL/CONT

VISUAL/SYNT

VISUAL/PLAN

VISUAL/PERS

FILTER/WAVE

COMPAR/WAVE

PLOT/SNR

PLOT/COR

DIRECT/WAVE

CITTERT/WAVE

GRAD/WAVE

LUCY/WAVE

TUTORIAL/WAVE

TRAN1D/WAVE

REC1D/WAVE

Petra Nass
1999-06-15