mrdwt.m
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- 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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