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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 <[email protected]>
%
%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 [email protected] or (713) 348-6173
%
%Change History:
%
%Modification #1
%Mon Aug 7 14:26:26 CDT 1995
%Rebecca Hindman <[email protected]>
%Added L to function line so that it can be displayed as an output
%
%Thursday Mar 2 2000
% Added Example 2
% Felix Fernandes <[email protected]>