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2维小波变换经典程序
% FWT_DB.M;
% 此示意程序用DWT实现二维小波变换
% 编程时间2004-4-10,编程人沙威
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear;clc;
T=256;
%
图像维数
SUB_T=T/2;
%
子图维数
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.调原始图像矩阵loadwbarb; % 下载图像f=X; % 原始图像
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.进行二维小波分解
l=wfilters(db10,l);
%
db10(消失矩为10)低通分解滤波器冲击响应(长度为20)
L=T-length(l);
l_zeros=[l,zeros(1,L)];
%
矩阵行数与输入图像一致,为2的整数幂
h=wfilters(db10,h);
%
db10(消失矩为10)高通分解滤波器冲击响应(长度为20)
h_zeros=[h,zeros(1,L)];
%
矩阵行数与输入图像一致,为2的整数幂
fori=1:T; % 列变换
row(1:SUB_T,i)=dyaddown(ifft(fft(l_zeros).*fft(f(:,i)))).; % 圆周卷积-FFT
row(SUB_T+1:T,i)=dyaddown(ifft(fft(h_zeros).*fft(f(:,i)))).; % 圆周卷积-FFT
end;
forj=1:T; % 行变换
line(j,1:SUB_T)=dyaddown(ifft(fft(l_zeros).*fft(row(j,:)))); % 圆周卷积-FFTline(j,SUB_T+1:T)=dyaddown(ifft(fft(h_zeros).*fft(row(j,:)))); % 圆周卷积-FFT
end;
decompose_pic=line; % 分解矩阵
% 图像分为四块
lt_pic=decompose_pic(1:SUB_T,1:SUB_T); % 在矩阵左上方为低频分量--fi(x)*fi(y)rt_pic=decompose_pic(1:SUB_T,SUB_T+1:T); % 矩阵右上为--fi(x)*psi(y)lb_pic=decompose_pic(SUB_T+1:T,1:SUB_T); % 矩阵左下为--psi(x)*fi(y)rb_pic=decompose_pic(SUB_T+1:T,SUB_T+1:T); % 右下方为高频分量--psi(x)*psi(y)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 3.分解结果显示figure(1);colormap(map);subplot(2,1,1);
image(f); % 原始图像
title(originalpic);
subplot(2,1,2);
image(abs(decompose_pic));
%
分解后图像
title(decomposedpic);
figure(2);
colormap(map);
subplot(2,2,1);
image(abs(lt_pic)); % 左上方为低频分量--fi(x)*fi(y)title(\Phi(x)*\Phi(y));
subplot(2,2,2);
image(abs(rt_pic)); % 矩阵右上为--fi(x)*psi(y)title(\Phi(x)*\Psi(y));
subplot(2,2,3);
image(abs(lb_pic)); % 矩阵左下为--psi(x)*fi(y)title(\Psi(x)*\Phi(y));
subplot(2,2,4);
image(abs(rb_pic)); % 右下方为高频分量--psi(x)*psi(y)title(\Psi(x)*\Psi(y));
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 5.重构源图像及结果显示
%construct_pic=decompose_matrix*decompose_pic*decom
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