压缩比为8:1的灰度图DCT压缩MATLAB代码

以下是MATLAB代码实现8:1的灰度图DCT压缩，其中我们使用了JPEG标准中的量化矩阵，并采用了Huffman编码进行熵编码：

% 读入原始图像
I = imread('lena_gray.png');

% 将灰度图像分成大小相等的块
block_size = 8;
[M, N] = size(I);
Mb = floor(M/block_size);
Nb = floor(N/block_size);
blocks = zeros(block_size, block_size, Mb*Nb);
for i = 1:Mb
    for j = 1:Nb
        idx = (i-1)*Nb+j;
        blocks(:,:,idx) = double(I((i-1)*block_size+1:i*block_size, (j-1)*block_size+1:j*block_size));
    end
end

% 定义JPEG标准中的量化矩阵
Q = [
    16  11  10  16  24  40  51  61;
    12  12  14  19  26  58  60  55;
    14  13  16  24  40  57  69  56;
    14  17  22  29  51  87  80  62;
    18  22  37  56  68 109 103  77;
    24  35  55  64  81 104 113  92;
    49  64  78  87 103 121 120 101;
    72  92  95  98 112 100 103  99
];

% 对每个块进行DCT变换
dct_blocks = zeros(block_size, block_size, Mb*Nb);
for i = 1:Mb*Nb
    dct_blocks(:,:,i) = dct2(blocks(:,:,i));
end

% 对频域系数矩阵进行量化处理
quant_blocks = zeros(block_size, block_size, Mb*Nb);
for i = 1:Mb*Nb
    quant_blocks(:,:,i) = round(dct_blocks(:,:,i)./Q);
end

% 对量化后的矩阵进行熵编码
huff_blocks = cell(1, Mb*Nb);
for i = 1:Mb*Nb
    huff_blocks{i} = huffmanenco(reshape(quant_blocks(:,:,i)', 1, []), huffmandict(1:256, Q(:)'));
end

% 将压缩后的数据进行解码和反量化
decode_blocks = zeros(block_size, block_size, Mb*Nb);
for i = 1:Mb*Nb
    decode_blocks(:,:,i) = reshape(huffmandeco(huff_blocks{i}, huffmandict(1:256, Q(:)')), block_size, block_size)';
    decode_blocks(:,:,i) = decode_blocks(:,:,i).*Q;
end

% 对近似块进行IDCT反变换
idct_blocks = zeros(block_size, block_size, Mb*Nb);
for i = 1:Mb*Nb
    idct_blocks(:,:,i) = idct2(decode_blocks(:,:,i));
end

% 将所有的块拼接起来，得到整个压缩后的图像
compressed_I = zeros(M, N);
for i = 1:Mb
    for j = 1:Nb
        idx = (i-1)*Nb+j;
        compressed_I((i-1)*block_size+1:i*block_size, (j-1)*block_size+1:j*block_size) = idct_blocks(:,:,idx);
    end
end

% 显示压缩前后的图像
figure, imshow(I), title('Original Image');
figure, imshow(uint8(compressed_I)), title('Compressed Image');

需要注意的是，由于MATLAB中的`huffmandict`函数在生成Huffman树时会对输入数据进行排序，因此我们需要将量化矩阵展成一维数组并按照从小到大的顺序排列，以保证压缩和解压缩时使用同一个Huffman字典。