【图像压缩】基于奇异值分解svd进行图像压缩matlab代码

 1 简介

根据奇异值分解的基本原理及其特点,给出了运用奇异值分解进行图像压缩的方法.通过简单的例子说明了该方法进行图像压缩的基本过程,给出了压缩流程.并通过MAT-LAB编程对实际图像进行处理,表明了该方法的有效性.

2 完整代码

% Read the image into A as a matrix of uint8clcclear allclose all[X,map] = imread('witchhead.jpg');Im = X;​% Convert image from uint8 to doubles for svdX = im2double(X);​% Seperate [U_r,S_r,V_r] = svd(X(:,:,1));[U_g,S_g,V_g] = svd(X(:,:,2));[U_b,S_b,V_b] = svd(X(:,:,3));​%=============================% Test Scripts%=============================​%confirmation checking for redout_red = U_r*S_r*V_r';red = X(:,:,1);​%-----------------------------​% S_r has size 640x1138, thus 640 diagonal valuessize(S_r)% Find the largest k singular valuesk = 30;redk = zeros(k,1);greenk = zeros(k,1);bluek = zeros(k,1);​% Discovered that the diagonal of the sum matrix is in orderfor i = 1:k    redk(i) = S_r(i,i);    greenk(i) = S_g(i,i);    bluek(i) = S_b(i,i);end​%-----------------------------​% Storage AnalysisinitialStorage = 640*1138;currentStorage = (640+1138)*k+k;​%-----------------------------​% Error Analysissume = 0;for i = 1:640    sume = sume + S_r(i,i) + S_g(i,i) + S_b(i,i);enderror = sum(redk+greenk+bluek) / sume;​%-----------------------------​NewImage_r = zeros(640,1138);NewImage_g = zeros(640,1138);NewImage_b = zeros(640,1138);for i = 1:k    NewImage_r = NewImage_r + redk(i)* U_r(:,i)*V_r(:,i)';    NewImage_g = NewImage_g + greenk(i) * U_g(:,i)*V_g(:,i)';    NewImage_b = NewImage_b + bluek(i) * U_b(:,i)*V_b(:,i)';end​%-----------------------------​% Normalize the matrices to fit the rgb formatfor i = 1:640    for j = 1:1138        if(NewImage_r(i,j) < 0)            NewImage_r(i,j) = 0;        end        if(NewImage_g(i,j) < 0)            NewImage_g(i,j) = 0;        end        if(NewImage_b(i,j) < 0)            NewImage_b(i,j) = 0;        end    endend​%-----------------------------​rgbImage = cat(3, NewImage_r, NewImage_g, NewImage_b);% image(rgbImage);% image(X);difference = rgbImasge-Xfiguresubplot(121)imshow(X,[]);title('原图')subplot(122)imshow(NewImage_b,[]);title('压缩后的图')​%-----------------------------​

3 仿真结果

4 参考文献

[1]胡乡峰, 卫金茂. 基于奇异值分解(SVD)的图像压缩[J]. 东北师大学报：自然科学版, 2006, 38(3):4.

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