【图像压缩】基于奇异值分解svd进行图像压缩matlab代码

% Read the image into A as a matrix of uint8 clc clear all close all [X,map] = imread(’witchhead.jpg’); Im = X; % Convert image from uint8 to doubles for svd X = 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 red out_red = U_r*S_r*V_r’; red = X(:,:,1); %----------------------------- % S_r has size 640x1138, thus 640 diagonal values size(S_r) % Find the largest k singular values k = 30; redk = zeros(k,1); greenk = zeros(k,1); bluek = zeros(k,1); % Discovered that the diagonal of the sum matrix is in order for i = 1:k redk(i) = S_r(i,i); greenk(i) = S_g(i,i); bluek(i) = S_b(i,i); end %----------------------------- % Storage Analysis initialStorage = 640*1138; currentStorage = (640+1138)*k+k; %----------------------------- % Error Analysis sume = 0; for i = 1:640 sume = sume + S_r(i,i) + S_g(i,i) + S_b(i,i); end error = 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 format for 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 end end %----------------------------- rgbImage = cat(3, NewImage_r, NewImage_g, NewImage_b); % image(rgbImage); % image(X); difference = rgbImasge-X figure subplot(121) imshow(X,[]);title(’原图’) subplot(122) imshow(NewImage_b,[]);title(’压缩后的图’) %-----------------------------