灰度图像压缩：

代码：

I=imread('F:4.jpg');
% I=imresize(I,[256 256]);
I=double(I);
[U,S,V]=svd(I);
for k=1:100
    Ik=U(:,1:k)*S(1:k,1:k)*V(:,1:k)';
%     Ik=im2uint8(Ik);
    figure;imshow(Ik);
end

运行结果：

省略......

彩色图像压缩：

代码：

clc
clear all
I=imread('E:tets.jpg');
imshow(I);
[m,n]=size(I(:,:,1));
A0=zeros(m,n);
A1=double(I(:,:,1));
A2=double(I(:,:,2));
A3=double(I(:,:,3));
%svdQ
A=[A0 A1 A2 A3];
[U S V]=svdQ(A);
k=1;
Sx=S(1:k,1:k);
while(sum(sum(Sx))/sum(sum(S))<0.95)
    %设置k的大小，当图像精度小于0.95时，k+1继续压缩下一个图像，直到图像精度大于0.95时停止
    J=timesQ(U(:,[1:k,m+1:m+k,2*m+1:2*m+k,3*m+1:3*m+k]),[Sx,zeros(k,3*k)]);
    J=timesQ(J,transQ(V(:,[1:k,n+1:n+k,2*n+1:2*n+k,3*n+1:3*n+k])));
    %refactor
    [jm,jn]=size(J);
    jn=jn/4;
    X(:,:,2)=J(:,jn+1:2*jn);
    X(:,:,1)=J(:,2*jn+1:3*jn);
    X(:,:,3)=J(:,3*jn+1:4*jn);
     figure ;
     imshow(uint8(X));
     k=k+1;
     Sx=S(1:k,1:k);
end

运行结果：

省略......