<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN"> <!--Converted with LaTeX2HTML 98.1p1 release (March 2nd, 1998) originally by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds * revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan * with significant contributions from: Jens Lippmann, Marek Rouchal, Martin Wilck and others --> <HTML> <HEAD> <TITLE>The Wavelet Transform</TITLE> <META NAME="description" CONTENT="The Wavelet Transform"> <META NAME="keywords" CONTENT="vol2"> <META NAME="resource-type" CONTENT="document"> <META NAME="distribution" CONTENT="global"> <META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso-8859-1"> <LINK REL="STYLESHEET" HREF="vol2.css"> <LINK REL="next" HREF="node370.html"> <LINK REL="previous" HREF="node307.html"> <LINK REL="up" HREF="vol2.html"> <LINK REL="next" HREF="node309.html"> </HEAD> <BODY > <!--Navigation Panel--> <A NAME="tex2html5252" HREF="node309.html"> <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="icons.gif/next_motif.gif"></A> <A NAME="tex2html5249" HREF="vol2.html"> <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="icons.gif/up_motif.gif"></A> <A NAME="tex2html5243" HREF="node307.html"> <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="icons.gif/previous_motif.gif"></A> <A NAME="tex2html5251" HREF="node1.html"> <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="icons.gif/contents_motif.gif"></A> <BR> <B> Next:</B> <A NAME="tex2html5253" HREF="node309.html">Introduction</A> <B> Up:</B> <A NAME="tex2html5250" HREF="vol2.html">No Title</A> <B> Previous:</B> <A NAME="tex2html5244" HREF="node307.html">Bibliography</A> <BR> <BR> <!--End of Navigation Panel--> <H1><A NAME="SECTION002000000000000000000"> The Wavelet Transform</A> </H1> <P> <BR><HR> <!--Table of Child-Links--> <A NAME="CHILD_LINKS"> </A> <UL> <LI><A NAME="tex2html5254" HREF="node309.html">Introduction</A> <LI><A NAME="tex2html5255" HREF="node310.html">The continuous wavelet transform</A> <LI><A NAME="tex2html5256" HREF="node311.html">Examples of Wavelets</A> <UL> <LI><A NAME="tex2html5257" HREF="node312.html">Morlet's Wavelet</A> <UL> <LI><A NAME="tex2html5258" HREF="node313.html">Mexican Hat</A> </UL> </UL> <LI><A NAME="tex2html5259" HREF="node314.html">The discrete wavelet transform</A> <UL> <LI><A NAME="tex2html5260" HREF="node315.html">Introduction</A> <LI><A NAME="tex2html5261" HREF="node316.html">Multiresolution Analysis</A> <LI><A NAME="tex2html5262" HREF="node317.html">The <EM>à trous</EM> algorithm </A> <LI><A NAME="tex2html5263" HREF="node318.html">Pyramidal Algorithm</A> <UL> <LI><A NAME="tex2html5264" HREF="node319.html">The Laplacian Pyramid</A> <LI><A NAME="tex2html5265" HREF="node320.html">Pyramidal Algorithm with one Wavelet</A> </UL> <LI><A NAME="tex2html5266" HREF="node321.html">Multiresolution with scaling functions with a frequency cut-off</A> <UL> <LI><A NAME="tex2html5267" HREF="node322.html">The Wavelet transform using the Fourier transform</A> <LI><A NAME="tex2html5268" HREF="node323.html">The Reconstruction</A> </UL> </UL> <LI><A NAME="tex2html5269" HREF="node324.html">Visualization of the Wavelet Transform</A> <UL> <LI><A NAME="tex2html5270" HREF="node325.html">Visualisation of the first class</A> <LI><A NAME="tex2html5271" HREF="node326.html">Visualisation of the second class</A> <LI><A NAME="tex2html5272" HREF="node327.html">Visualisation of the third class</A> </UL> <LI><A NAME="tex2html5273" HREF="node328.html">Noise reduction from the wavelet transform</A> <UL> <LI><A NAME="tex2html5274" HREF="node329.html">The convolution from the continuous wavelet transform</A> <LI><A NAME="tex2html5275" HREF="node330.html">The Wiener-like filtering in the wavelet space</A> <LI><A NAME="tex2html5276" HREF="node331.html">Hierarchical Wiener filtering</A> <LI><A NAME="tex2html5277" HREF="node332.html">Adaptive filtering from the wavelet transform</A> <LI><A NAME="tex2html5278" HREF="node333.html">Hierarchical adaptive filtering</A> </UL> <LI><A NAME="tex2html5279" HREF="node334.html">Comparison using a multiresolution quality criterion</A> <LI><A NAME="tex2html5280" HREF="node335.html">Deconvolution</A> <UL> <LI><A NAME="tex2html5281" HREF="node336.html">Introduction</A> <LI><A NAME="tex2html5282" HREF="node337.html">Regularization in the wavelet space</A> <LI><A NAME="tex2html5283" HREF="node338.html">Tikhonov's regularization and multiresolution analysis</A> <LI><A NAME="tex2html5284" HREF="node339.html">Regularization from significant structures</A> <UL> <LI><A NAME="tex2html5285" HREF="node340.html">Regularization of Van Cittert's algorithm</A> <LI><A NAME="tex2html5286" HREF="node341.html">Regularization of the one-step gradient method</A> <LI><A NAME="tex2html5287" HREF="node342.html">Regularization of Lucy's algorithm</A> <LI><A NAME="tex2html5288" HREF="node343.html">Convergence</A> </UL> </UL> <LI><A NAME="tex2html5289" HREF="node344.html">The wavelet context in MIDAS</A> <UL> <LI><A NAME="tex2html5290" HREF="node345.html">Introduction</A> <LI><A NAME="tex2html5291" HREF="node346.html">Commands Description</A> <UL> <LI><A NAME="tex2html5292" HREF="node347.html">TRANSF/WAVE</A> <LI><A NAME="tex2html5293" HREF="node348.html">RECONS/WAVE</A> <LI><A NAME="tex2html5294" HREF="node349.html">HEADER/WAVE</A> <LI><A NAME="tex2html5295" HREF="node350.html">INFO/WAVE</A> <LI><A NAME="tex2html5296" HREF="node351.html">EXTRAC/WAVE</A> <LI><A NAME="tex2html5297" HREF="node352.html">ENTER/WAVE</A> <LI><A NAME="tex2html5298" HREF="node353.html">VISUAL/WAVE</A> <LI><A NAME="tex2html5299" HREF="node354.html">VISUAL/CUB</A> <LI><A NAME="tex2html5300" HREF="node355.html">VISUAL/CONT</A> <LI><A NAME="tex2html5301" HREF="node356.html">VISUAL/SYNT</A> <LI><A NAME="tex2html5302" HREF="node357.html">VISUAL/PLAN</A> <LI><A NAME="tex2html5303" HREF="node358.html">VISUAL/PERS</A> <LI><A NAME="tex2html5304" HREF="node359.html">FILTER/WAVE</A> <LI><A NAME="tex2html5305" HREF="node360.html">COMPAR/WAVE</A> <LI><A NAME="tex2html5306" HREF="node361.html">PLOT/SNR</A> <LI><A NAME="tex2html5307" HREF="node362.html">PLOT/COR</A> <LI><A NAME="tex2html5308" HREF="node363.html">DIRECT/WAVE</A> <LI><A NAME="tex2html5309" HREF="node364.html">CITTERT/WAVE</A> <LI><A NAME="tex2html5310" HREF="node365.html">GRAD/WAVE</A> <LI><A NAME="tex2html5311" HREF="node366.html">LUCY/WAVE</A> <LI><A NAME="tex2html5312" HREF="node367.html">TUTORIAL/WAVE</A> <LI><A NAME="tex2html5313" HREF="node368.html">TRAN1D/WAVE</A> <LI><A NAME="tex2html5314" HREF="node369.html">REC1D/WAVE</A> </UL></UL></UL> <!--End of Table of Child-Links--> <BR><HR> <ADDRESS> <I>Petra Nass</I> <BR><I>1999-06-15</I> </ADDRESS> </BODY> </HTML>
