【matlab代码】基于DCT变换矩阵法-图像压缩与还原

clear;close all;clc; % 图像读取与灰度化 gray = rgb2gray(imread('lena.jpg')); % 将图像数据uint8类型转换为double类型并进行归一化 doubleGray = im2double(gray); % 定义DCT变换矩阵 t = dctmtx(8); % 将原图的每个8x8块进行DCT变换 y = blkproc(doubleGray, [8 8], 'P1*x*P2', t, t'); figure(2), imshow(log(abs(y)), []), title('DCT系数'); % 定义量化矩阵 mask1 = [1 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0]; mask2 = [1 1 0 0 0 0 0 0; 1 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0]; mask3 = [1 1 1 0 0 0 0 0; 1 1 0 0 0 0 0 0; 1 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0]; mask4 = [1 1 1 1 0 0 0 0; 1 1 1 0 0 0 0 0; 1 1 0 0 0 0 0 0; 1 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0]; mask5 = [1 1 1 1 1 0 0 0; 1 1 1 1 0 0 0 0; 1 1 1 0 0 0 0 0; 1 1 0 0 0 0 0 0; 1 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0]; mask6 = [1 1 1 1 1 1 0 0; 1 1 1 1 1 0 0 0; 1 1 1 1 0 0 0 0; 1 1 1 0 0 0 0 0; 1 1 0 0 0 0 0 0; 1 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0]; mask7 = [1 1 1 1 1 1 1 0; 1 1 1 1 1 1 0 0; 1 1 1 1 1 0 0 0; 1 1 1 1 0 0 0 0; 1 1 1 0 0 0 0 0; 1 1 0 0 0 0 0 0; 1 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0]; mask8 = [1 1 1 1 1 1 1 1; 1 1 1 1 1 1 1 0; 1 1 1 1 1 1 0 0; 1 1 1 1 1 0 0 0; 1 1 1 1 0 0 0 0; 1 1 1 0 0 0 0 0; 1 1 0 0 0 0 0 0; 1 0 0 0 0 0 0 0]; mask9 = [0 0 1 1 1 1 1 1; 0 1 1 1 1 1 1 1; 1 1 1 1 1 1 1 1; 1 1 1 1 1 1 1 1; 1 1 1 1 1 1 1 1; 1 1 1 1 1 1 1 1; 1 1 1 1 1 1 1 1; 1 1 1 1 1 1 1 1]; mask10= [0 0 0 0 1 1 1 1; 0 0 0 1 1 1 1 1; 0 0 1 1 1 1 1 1; 0 1 1 1 1 1 1 1; 1 1 1 1 1 1 1 1; 1 1 1 1 1 1 1 1; 1 1 1 1 1 1 1 1; 1 1 1 1 1 1 1 1]; mask11= [0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 1; 0 0 0 0 0 0 1 1; 0 0 0 0 0 1 1 1; 0 0 0 0 1 1 1 1; 0 0 0 1 1 1 1 1; 0 0 1 1 1 1 1 1; 0 1 1 1 1 1 1 1]; maskall=[1 1 1 1 1 1 1 1; 1 1 1 1 1 1 1 1; 1 1 1 1 1 1 1 1; 1 1 1 1 1 1 1 1; 1 1 1 1 1 1 1 1; 1 1 1 1 1 1 1 1; 1 1 1 1 1 1 1 1; 1 1 1 1 1 1 1 1]; % 对DCT系数矩阵进行量化 my1 = blkproc(y, [8 8], 'P1.*x', mask1); my2 = blkproc(y, [8 8], 'P1.*x', mask2); my3 = blkproc(y, [8 8], 'P1.*x', mask3); my4 = blkproc(y, [8 8], 'P1.*x', mask4); my5 = blkproc(y, [8 8], 'P1.*x', mask5); my6 = blkproc(y, [8 8], 'P1.*x', mask6); my7 = blkproc(y, [8 8], 'P1.*x', mask7); my8 = blkproc(y, [8 8], 'P1.*x', mask8); my9 = blkproc(y, [8 8], 'P1.*x', mask9); my10= blkproc(y, [8 8], 'P1.*x', mask10); my11= blkproc(y, [8 8], 'P1.*x', mask11); myall=blkproc(y, [8 8], 'P1.*x', maskall); % 对每个8x8块进行IDCT变换，恢复图像 y1 = blkproc(my1, [8 8], 'P1*x*P2', t', t); y2 = blkproc(my2, [8 8], 'P1*x*P2', t', t); y3 = blkproc(my3, [8 8], 'P1*x*P2', t', t); y4 = blkproc(my4, [8 8], 'P1*x*P2', t', t); y5 = blkproc(my5, [8 8], 'P1*x*P2', t', t); y6 = blkproc(my6, [8 8], 'P1*x*P2', t', t); y7 = blkproc(my7, [8 8], 'P1*x*P2', t', t); y8 = blkproc(my8, [8 8], 'P1*x*P2', t', t); y9 = blkproc(my9, [8 8], 'P1*x*P2', t', t); y10= blkproc(my10,[8 8], 'P1*x*P2', t', t); y11= blkproc(my11,[8 8], 'P1*x*P2', t', t); yall=blkproc(myall,[8 8],'P1*x*P2', t', t); % 显示被压缩的图像与解压缩的图像 figure(3), imshow(doubleGray), title('原图'); figure(4), imshow(y1), title('量化系数为1的压缩图像'); figure(5), imshow(y2), title('量化系数为2的压缩图像'); figure(6), imshow(y3), title('量化系数为3的压缩图像'); figure(7), imshow(y4), title('量化系数为4的压缩图像'); figure(8), imshow(y5), title('量化系数为5的压缩图像'); figure(9), imshow(y6), title('量化系数为6的压缩图像'); figure(10),imshow(y7), title('量化系数为7的压缩图像'); figure(11),imshow(y8), title('量化系数为8的压缩图像'); figure(12),imshow(y9), title('舍弃低频2位的压缩图像'); figure(13),imshow(y10),title('舍弃低频4位的压缩图像'); figure(14),imshow(y11),title('舍弃低频8位的压缩图像'); figure(15),imshow(yall),title('保留所有'); % 输出对应MSE值 shape = size(doubleGray); disp('量化系数为1的压缩图像MSE: '); se = (doubleGray-y1).^2; sum(se(:)) / (shape(1)*shape(2)) disp('量化系数为2的压缩图像MSE: '); se = (doubleGray-y2).^2; sum(se(:)) / (shape(1)*shape(2)) disp('量化系数为3的压缩图像MSE: '); se = (doubleGray-y3).^2; sum(se(:)) / (shape(1)*shape(2)) disp('量化系数为4的压缩图像MSE: '); se = (doubleGray-y4).^2; sum(se(:)) / (shape(1)*shape(2)) disp('量化系数为5的压缩图像MSE: '); se = (doubleGray-y5).^2; sum(se(:)) / (shape(1)*shape(2)) disp('量化系数为6的压缩图像MSE: '); se = (doubleGray-y6).^2; sum(se(:)) / (shape(1)*shape(2)) disp('量化系数为7的压缩图像MSE: '); se = (doubleGray-y7).^2; sum(se(:)) / (shape(1)*shape(2)) disp('量化系数为8的压缩图像MSE: '); se = (doubleGray-y8).^2; sum(se(:)) / (shape(1)*shape(2)) disp('舍弃低频2位的压缩图像MSE: '); se = (doubleGray-y9).^2; sum(se(:)) / (shape(1)*shape(2)) disp('舍弃低频4位的压缩图像MSE: '); se = (doubleGray-y10).^2; sum(se(:)) / (shape(1)*shape(2)) disp('舍弃低频8位的压缩图像MSE: '); se = (doubleGray-y11).^2; sum(se(:)) / (shape(1)*shape(2)) disp('保留全部MSE: '); se = (doubleGray-yall).^2; sum(se(:)) / (shape(1)*shape(2))