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Highlights from
Wavelets Based Denoising

Wavelets Based Denoising

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25 Nov 2004 (Updated )

This program shows wavelets based denoising of audio file and arbitrary signals.

mrdwt(x,h,L);
function [yl,yh,L] = mrdwt(x,h,L);
%    [yl,yh,L] = mrdwt(x,h,L);
% 
%    Function computes the redundant discrete wavelet transform y
%    for a 1D  or 2D input signal. (Redundant means here that the
%    sub-sampling after each stage is omitted.) yl contains the
%    lowpass and yh the highpass components. In the case of a 2D
%    signal, the ordering in yh is 
%    [lh hl hh lh hl ... ] (first letter refers to row, second to
%    column filtering). 
%
%    Input:
%	     x : finite length 1D or 2D signal (implicitly periodized)
%       h : scaling filter
%       L : number of levels. In the case of a 1D 
%           length(x) must be  divisible by 2^L;
%           in the case of a 2D signal, the row and the
%           column dimension must be divisible by 2^L.
%           If no argument is
%           specified, a full DWT is returned for maximal possible L.
%   
%    Output:
%       yl : lowpass component
%       yh : highpass components
%       L  : number of levels
%
%  HERE'S AN EASY WAY TO RUN THE EXAMPLES:
%  Cut-and-paste the example you want to run to a new file 
%  called ex.m, for example. Delete out the % at the beginning 
%  of each line in ex.m (Can use search-and-replace in your editor
%  to replace it with a space). Type 'ex' in matlab and hit return.
%
%
%    Example 1::
%    x = makesig('Leopold',8);
%    h = daubcqf(4,'min');
%    L = 1;
%    [yl,yh,L] = mrdwt(x,h,L)
%    yl =  0.8365  0.4830 0 0 0 0 -0.1294 0.2241
%    yh = -0.2241 -0.1294 0 0 0 0 -0.4830 0.8365
%    L = 1
%    Example 2:
%    load lena;
%    h = daubcqf(4,'min');
%    L = 2;
%    [ll_lev2,yh,L] = mrdwt(lena,h,L); % lena is a 256x256 matrix
%    N = 256;
%    lh_lev1 = yh(:,1:N); 
%    hl_lev1 = yh(:,N+1:2*N); 
%    hh_lev1 = yh(:,2*N+1:3*N);
%    lh_lev2 = yh(:,3*N+1:4*N); 
%    hl_lev2 = yh(:,4*N+1:5*N); 
%    hh_lev2 = yh(:,5*N+1:6*N);
%    figure; colormap(gray); imagesc(lena); title('Original Image');
%    figure; colormap(gray); imagesc(ll_lev2); title('LL Level 2');
%    figure; colormap(gray); imagesc(hh_lev2); title('HH Level 2');
%    figure; colormap(gray); imagesc(hl_lev2); title('HL Level 2');
%    figure; colormap(gray); imagesc(lh_lev2); title('LH Level 2');
%    figure; colormap(gray); imagesc(hh_lev1); title('HH Level 1');
%    figure; colormap(gray); imagesc(hl_lev2); title('HL Level 1');
%    figure; colormap(gray); imagesc(lh_lev2); title('LH Level 1');
%           
%    See also: mdwt, midwt, mirdwt
%
%    Warning! min(size(x))/2^L should be greater than length(h)
%

%File Name: mrdwt.m
%Last Modification Date: 08/07/95	15:14:47
%Current Version: mrdwt.m	2.4
%File Creation Date: Wed Oct 19 10:51:58 1994
%Author: Markus Lang  <lang@jazz.rice.edu>
%
%Copyright (c) 2000 RICE UNIVERSITY. All rights reserved.
%Created by Markus Lang, Department of ECE, Rice University. 
%
%This software is distributed and licensed to you on a non-exclusive 
%basis, free-of-charge. Redistribution and use in source and binary forms, 
%with or without modification, are permitted provided that the following 
%conditions are met:
%
%1. Redistribution of source code must retain the above copyright notice, 
%   this list of conditions and the following disclaimer.
%2. Redistribution in binary form must reproduce the above copyright notice, 
%   this list of conditions and the following disclaimer in the 
%   documentation and/or other materials provided with the distribution.
%3. All advertising materials mentioning features or use of this software 
%   must display the following acknowledgment: This product includes 
%   software developed by Rice University, Houston, Texas and its contributors.
%4. Neither the name of the University nor the names of its contributors 
%   may be used to endorse or promote products derived from this software 
%   without specific prior written permission.
%
%THIS SOFTWARE IS PROVIDED BY WILLIAM MARSH RICE UNIVERSITY, HOUSTON, TEXAS, 
%AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, 
%BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS 
%FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL RICE UNIVERSITY 
%OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, 
%EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, 
%PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; 
%OR BUSINESS INTERRUPTIONS) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, 
%WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR 
%OTHERWISE), PRODUCT LIABILITY, OR OTHERWISE ARISING IN ANY WAY OUT OF THE 
%USE OF THIS SOFTWARE,  EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
%
%For information on commercial licenses, contact Rice University's Office of 
%Technology Transfer at techtran@rice.edu or (713) 348-6173
%
%Change History:
% 
%Modification #1
%Mon Aug  7 14:26:26 CDT 1995
%Rebecca Hindman <hindman@ece.rice.edu>
%Added L to function line so that it can be displayed as an output
% 
%Thursday Mar 2 2000
% Added Example 2
% Felix Fernandes <felixf@rice.edu>


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