沙威教授用小波变换当测量矩阵的OMP算法，压缩感知

% 此示意程序用DWT实现二维小波变换 % 编程人 沙威(Wei Sha) 安徽大学(Anhui University) ws108@ahu.edu.cn %%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%% 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');