matlab 二维小波变换程序

MATLAB2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 %%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%% clear;clc; T=256;       %  图像维数 SUB_T=T/2;   %  子图维数 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %  1.调原始图像矩阵 load wbarb;  %  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 for i=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; for j=1:T;   %  行变换     line(j,1:SUB_T)=dyaddown( ifft( fft(l_zeros).*fft(row(j,:)) ) );    %  圆周卷积<->FFT     line(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('original pic'); subplot(2,1,2); image(abs(decompose_pic));  %  分解后图像 title('decomposed pic'); 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*decompose_matrix; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% l_re=l_zeros(end:-1:1);   %  重构低通滤波 l_r=circshift(l_re',1)';  %  位置调整 h_re=h_zeros(end:-1:1);   %  重构高通滤波 h_r=circshift(h_re',1)';  %  位置调整   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% top_pic=[lt_pic,rt_pic];  %  图像上半部分 t=0; for i=1:T;  %  行插值低频       if (mod(i,2)==0)         topll(i,:)=top_pic(t,:); %  偶数行保持     else         t=t+1;         topll(i,:)=zeros(1,T);   %  奇数行为零     end end; for i=1:T;  %  列变换     topcl_re(:,i)=ifft( fft(l_r).*fft(topll(:,i)') )';  %  圆周卷积<->FFT end;   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% bottom_pic=[lb_pic,rb_pic];  %  图像下半部分 t=0; for i=1:T;  %  行插值高频     if (mod(i,2)==0)         bottomlh(i,:)=bottom_pic(t,:);  %  偶数行保持     else         bottomlh(i,:)=zeros(1,T);       %  奇数行为零         t=t+1;     end end; for i=1:T; %  列变换     bottomch_re(:,i)=ifft( fft(h_r).*fft(bottomlh(:,i)') )';  %  圆周卷积<->FFT end;   construct1=bottomch_re+topcl_re;  %  列变换重构完毕   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% left_pic=construct1(:,1:SUB_T);   %  图像左半部分 t=0; for i=1:T;  %  列插值低频       if (mod(i,2)==0)         leftll(:,i)=left_pic(:,t); %  偶数列保持     else         t=t+1;         leftll(:,i)=zeros(T,1);    %  奇数列为零     end end; for i=1:T;  %  行变换     leftcl_re(i,:)=ifft( fft(l_r).*fft(leftll(i,:)) );  %  圆周卷积<->FFT end;     %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% right_pic=construct1(:,SUB_T+1:T);  %  图像右半部分 t=0; for i=1:T;  %  列插值高频     if (mod(i,2)==0)         rightlh(:,i)=right_pic(:,t);  %  偶数列保持     else         rightlh(:,i)=zeros(T,1);      %  奇数列为零         t=t+1;     end end; for i=1:T; %  行变换     rightch_re(i,:)=ifft( fft(h_r).*fft(rightlh(i,:)) );  %  圆周卷积<->FFT end;   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% construct_pic=rightch_re+leftcl_re;  %  重建全部图像   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %  结果显示 figure(3); colormap(map); subplot(2,1,1); image(f);  %  源图像显示 title('original pic'); subplot(2,1,2); image(abs(construct_pic));   %  重构源图像显示 title('reconstructed pic'); error=abs(construct_pic-f);  %  重构图形与原始图像误值 figure(4); mesh(error);  %  误差三维图像 title('absolute error display');