基于SVD分解的PCA降维图像重建MATLAB仿真+仿真操作录像

clc; clear; close all; warning off; addpath(genpath(pwd)); img = imread('x.jpg'); figure(1); subplot(1,2,1); imshow(img); title('Original'); % Do SVD on grayscale NxN matrix shape = size(img); U = zeros(shape); S = zeros(shape); V = zeros(shape); for i = 1:3 [U(:,:,i),S(:,:,i),V(:,:,i)] = svd(im2double(img(:,:,i))); end % Contains sub-portion of components Ug = zeros(shape); Sg = zeros(shape); Vgt = zeros(shape); Vt = zeros(shape); for i = 1:3 Vt(:,:,i) = V(:,:,i)'; end % Regenerate from components (for varying sub-portions p) N = 10; for p = 1:N regenerated_img = zeros(shape); for i = 1:3 Ug(:, 1:p, i) = U(:, 1:p, i); Sg(1:p, 1:p, i) = S(1:p, 1:p, i); Vgt(1:p, :, i) = Vt(1:p, :, i); regenerated_img(:,:,i) = Ug(:,:,i) * Sg(:,:,i) * Vgt(:,:,i); end mses(p) = mean2(double(img)-regenerated_img); figure; imshow(regenerated_img,[]); end figure; plot(mses,'b-o');