PCA图像压缩的matlab实现

PCA

function pca_testclear;close all;img=imread('lena.png');           figure(1),subplot(121),imshow(img,[]);title('Original Image');[M N] = size(img);f = double(img);bs = 16;   %图像块尺寸p = 30;    %保留的维数% PCA图像压缩g = im2col(f, [bs bs], 'distinct'); %将图像块转换成列矢量表示g_m = ones(size(g,1),1)*mean(g);    %计算每个块的灰度均值g = g - g_m;[E D]=fun_pca(g);E_proj = E(:,1:p);   %取最大的p个特征值所对应的特征矢量进行降维g_proj = g'*E_proj;  %从bs*bs维映射到p维% 恢复图像g_rec = g_proj*E_proj';s = g_rec' + g_m;s = col2im(s, [bs bs], [M N], 'distinct');figure(1),subplot(122),imshow(s,[]);title('Recovered Image');function [E,D] = fun_pca(X)% do PCA on image patches% INPUT variables:% X                  matrix with image patches as columns% OUTPUT variables:% E                  特征矢量（第一列对应最大特征值）% D                  特征值（按下降顺序排列）% Calculate the eigenvalues and eigenvectorscovarianceMatrix = X*X'/(size(X,2)-1);[E, D] = eig(covarianceMatrix);% Sort the eigenvalues and recompute matrices[d_out,order] = sort(diag(D),'descend');E = E(:,order);d = diag(D); D = diag(d(order));