dct_2d.m

用离散余弦变换实现JPEG编码

%二维DCT变换
function y = dct_2D(x)
%获取图像矩阵大小
size_x = size(x);                      
height = size_x(1,1);                  
width = size_x(1,2);                   
%计算所需计算的2的次方的矩阵
h2 = ceil(log2(height));             
w2 = ceil(log2(width));              
%实际计算的矩阵大小(h,w)
h = 2^h2;                             
w = 2^w2;                             
%得到补0的矩阵
X = zeros(h,w);
X(1:height,1:width) = x;      
%可分离，一维一维计算
%中间结果Y
Y = zeros(h,w);                       
for i=1:h
    Y(i,:) = dct_1D(X(i,:));
end
%最终结果y
y = zeros(h,w);                       
for i=1:w
    y(:,i) = ( dct_1D(Y(:,i)') )';
end