MATLAB实现的基于压缩感知的图像处理

1. 参数设置

% 图像参数
imageSize = [256, 256]; % 图像大小
patchSize = [8, 8]; % 图像块大小
stepSize = 4; % 步长% 压缩感知参数
numAtoms = 256; % 字典中原子数量
numIterations = 10; % 稀疏分解迭代次数
lambda = 0.1; % 稀疏正则化参数

2. 读取并预处理图像

% 读取图像
I = imread('example_image.png'); % 替换为实际图像路径
I = imresize(I, imageSize); % 调整图像大小
I = im2double(I); % 转换为双精度浮点数% 添加噪声（可选）
noiseVar = 0.01; % 噪声方差
I_noisy = I + sqrt(noiseVar) * randn(imageSize); % 添加高斯噪声

3. 图像稀疏分解

% 初始化字典
D = randn(patchSize(1) * patchSize(2), numAtoms); % 随机初始化字典
D = D / sqrt(sum(D.^2, 1)); % 归一化字典原子% 稀疏分解
for iter = 1:numIterations% 提取图像块patches = im2col(I_noisy, patchSize, 'sliding', stepSize);% 稀疏编码alpha = sparseCoding(patches, D, lambda);% 字典更新D = dictionaryUpdate(patches, alpha, D);
end

4. 图像重建

% 重建图像
reconstructed_patches = D * alpha;
I_reconstructed = col2im(reconstructed_patches, patchSize, imageSize, 'sliding', stepSize);

5. 显示结果

% 显示原始图像、含噪图像和重建图像
figure;
subplot(1, 3, 1);
imshow(I);
title('原始图像');subplot(1, 3, 2);
imshow(I_noisy);
title('含噪图像');subplot(1, 3, 3);
imshow(I_reconstructed);
title('重建图像');

参考代码 基于压缩感知的图像处理 youwenfan.com/contentcnl/81986.html

辅助函数

稀疏编码函数

function alpha = sparseCoding(patches, D, lambda)% 稀疏编码numPatches = size(patches, 2);numAtoms = size(D, 2);alpha = zeros(numAtoms, numPatches);for i = 1:numPatches% 使用L1正则化最小化问题求解稀疏表示alpha(:, i) = lasso(D, patches(:, i), 'Lambda', lambda, 'Alpha', 1);end
end

字典更新函数

function D = dictionaryUpdate(patches, alpha, D)% 字典更新numPatches = size(patches, 2);numAtoms = size(D, 2);for j = 1:numAtoms% 找到非零稀疏系数的索引idx = find(alpha(j, :) ~= 0);if ~isempty(idx)% 更新字典原子D(:, j) = patches(:, idx) * alpha(j, idx) / sum(abs(alpha(j, idx)));endend
end