当前位置：首页 > news >正文

基于DCT的彩色图像压缩MATLAB实现

news 2026/5/12 21:07:28

一、核心流程

基于DCT的图像压缩遵循JPEG标准的核心步骤，具体流程如下：

颜色空间转换：将RGB图像转换为YCbCr空间，分离亮度（Y）与色度（Cb/Cr）分量。
分块DCT变换：将每个通道划分为8×8块，进行二维DCT变换。
量化：根据人眼视觉特性设计量化表，对DCT系数进行量化。
熵编码：采用Zigzag扫描、游程编码和霍夫曼编码压缩量化后的数据。
解压缩：逆向执行熵解码、反量化、逆DCT变换，重构图像。

二、MATLAB代码实现

1. 颜色空间转换与分块

% 读取图像并转换为YCbCr
img = imread('lena.jpg');
if size(img,3) == 3img_ycbcr = rgb2ycbcr(img);Y = img_ycbcr(:,:,1);Cb = img_ycbcr(:,:,2);Cr = img_ycbcr(:,:,3);
elseY = img;Cb = [];Cr = [];
end% 分块处理（8x8）
block_size = 8;
[rows, cols] = size(Y);
num_blocks_row = ceil(rows / block_size);
num_blocks_col = ceil(cols / block_size);

2. DCT变换与量化

% 定义量化表（JPEG标准）
luminance_quant = [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];% DCT变换与量化函数
function quant_block = dct_quant(block, quant_table, quality)dct_block = dct2(block);scale = 100 / quality;  % 质量因子调整量化强度quant_block = round(dct_block ./ (quant_table * scale));
end% 对每个块进行DCT和量化
Y_compressed = zeros(size(Y));
for i = 1:num_blocks_rowfor j = 1:num_blocks_col% 提取块row = (i-1)*block_size + 1 : min(i*block_size, rows);col = (j-1)*block_size + 1 : min(j*block_size, cols);block = Y(row,col);% DCT与量化quant_block = dct_quant(block, luminance_quant, 80);Y_compressed(row,col) = quant_block;end
end

3. Zigzag扫描与熵编码

% Zigzag扫描
function zigzag_vec = zigzag_scan(block)zigzag_order = [1,2,6,7,15,16,28,29,3,5,8,14,17,27,30,43,4,9,13,18,26,31,42,44,10,12,19,25,32,41,45,54,11,20,24,33,40,46,53,21,23,34,39,48,52,55,22,35,38,47,51,56,29,50,60,61,62,63,64];flat_block = block(:);zigzag_vec = flat_block(zigzag_order(1:numel(flat_block)));
end% 示例：对量化后的块进行Zigzag扫描
zigzag_data = [];
for i = 1:block_sizefor j = 1:block_sizeblock = Y_compressed((i-1)*block_size+1:i*block_size, (j-1)*block_size+1:j*block_size);zigzag_data = [zigzag_data, zigzag_scan(block)];end
end

4. 霍夫曼编码

% 霍夫曼编码（使用MATLAB内置函数）
huff_dict = huffmandict([0:255], [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64]);
encoded_data = huffmandeco(zigzag_data, huff_dict);

5. 解压缩与逆变换

% 逆量化
dequant_block = quant_block .* (quant_table * scale);% 逆DCT变换
idct_block = idct2(dequant_block);% 合并块并转换回RGB
reconstructed_Y = zeros(rows,cols);
block_idx = 1;
for i = 1:num_blocks_rowfor j = 1:num_blocks_col% 提取逆量化块row = (i-1)*block_size + 1 : min(i*block_size, rows);col = (j-1)*block_size + 1 : min(j*block_size, cols);dequant_block = reshape(encoded_data(block_idx:block_idx+63), [8,8]);reconstructed_Y(row,col) = idct_block;block_idx = block_idx + 64;end
end% 合并通道并转换回RGB
reconstructed_img = cat(3, reconstructed_Y, Cb, Cr);
reconstructed_img = ycbcr2rgb(reconstructed_img);

三、性能评估

% 计算PSNR
original = im2double(img);
reconstructed = im2double(reconstructed_img);
mse = mean((original(:) - reconstructed(:)).^2);
psnr = 10 * log10(1 / mse);% 计算压缩率
original_size = rows * cols;
compressed_size = numel(encoded_data);
compression_ratio = original_size / compressed_size;disp(['PSNR: ', num2str(psnr), ' dB, 压缩率: ', num2str(compression_ratio), ':1']);