DCT变换（几个简单的MATLAB的例子）

原文地址：http://hi.baidu.com/huguosheng/item/06393d5744ee9f3795eb05f2

example 1(use real image):

A=imread('class_f.png');
imshow(A) %A is unit8(0,255)
C=dct2(A); %进行余弦变换
figure;
B=log(abs(C));
imshow(B)
colormap(jet(64)); %显示为64级灰度
colorbar; %显示颜色条，显示变换后的系数分布
C(abs(C)<10)=0; %将DCT变换后的系数值小于10的元素设为0
%E=idct2(C);
D=idct2(C)./255; %对DCT变换值归一化，进行余弦反变换???
figure;
imshow(D) ;
% imshow(uint8(E)); is the same as D=idct2(C)./255
% imshow(E,[]); is the same as D=idct2(C)./255

FF=abs(C)<10; %Compute the number of elements which are smaller than 10
sum(sum(FF)) %result:56632
GG=abs(C)>10; %Compute the number of elements which are larger than 10
sum(sum(GG)) %result:16025

example 2(use artifical image):
constant Image(low frequency image)
A=ones(5);
B=dct2(A)
A =

     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
after DCT transformation
     5     0     0     0     0
     0     0     0     0     0
     0     0     0     0     0
     0     0     0     0     0
     0     0     0     0     0
C=idct2(B) %reconstruction according to B


random image(high frequency image)
A=randn(5)
B=dct2(A)
A =

   -0.4326    1.1909   -0.1867    0.1139    0.2944
   -1.6656    1.1892    0.7258    1.0668   -1.3362
    0.1253   -0.0376   -0.5883    0.0593    0.7143
    0.2877    0.3273    2.1832   -0.0956    1.6236
   -1.1465    0.1746   -0.1364   -0.8323   -0.6918

ans =

    0.5853   -0.5033   -1.3505   -1.2524   -0.3519
    0.2492    0.1007   -0.4273    0.1201   -1.5079
   -0.8317    0.4357   -0.4183   -0.5794   -0.4022
    1.7697   -0.3482    1.3882   -0.3871    1.4934
   -1.0525    0.1744    1.7976    0.0521   -0.4997
B(abs(B)<0.1)=0;//0.1 is threshold
C=idct2(B);//reconstruction