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基于稀疏低秩分解的图像去噪MATLAB实现

news 2026/5/11 22:54:54

基于稀疏低秩分解的图像去噪MATLAB实现，包含RPCA（鲁棒主成分分析）和WNNM（加权核范数最小化）两种主流方法，并支持PSNR/SSIM性能评估：

一、RPCA稀疏低秩去噪（基于交替方向乘子法）

function [L, S] = rpca_denoise(M, lambda, mu, tol, max_iter)% RPCA图像去噪 输入:%   M - 含噪图像矩阵%   lambda - 稀疏项权重 (默认: 1/sqrt(max(size(M))))%   mu - 增强拉格朗日参数 (默认: 1.25/norm(M,2))%   tol - 收敛容差 (默认: 1e-7)%   max_iter - 最大迭代次数 (默认: 1000)% 输出:%   L - 低秩成分 (去噪后图像)%   S - 稀疏噪声if nargin < 2 || isempty(lambda)lambda = 1 / sqrt(max(size(M)));endif nargin < 3 || isempty(mu)mu = 1.25 / norm(M, 2);endif nargin < 4 || isempty(tol)tol = 1e-7;endif nargin < 5 || isempty(max_iter)max_iter = 1000;end[m, n] = size(M);L = zeros(m, n);S = zeros(m, n);Y = zeros(m, n);for iter = 1:max_iter% 更新L (奇异值收缩)[U, sigma, V] = svd(M - S + Y/mu, 'econ');sigma = diag(sigma);svp = length(find(sigma > 1/mu));if svp >= 1sigma = sigma(1:svp) - 1/mu;elsesvp = 1;sigma = 0;endL = U(:, 1:svp) * diag(sigma) * V(:, 1:svp)';% 更新S (软阈值)temp = M - L + Y/mu;S = sign(temp) .* max(abs(temp) - lambda/mu, 0);% 更新拉格朗日乘子Z = M - L - S;Y = Y + mu * Z;% 收敛判断err = norm(Z, 'fro') / norm(M, 'fro');if mod(iter, 50) == 0fprintf('RPCA迭代 %d, 误差: %.2e\n', iter, err);endif err < tolfprintf('RPCA在迭代 %d 收敛\n', iter);break;endend
end% 示例调用
clean_img = imread('lena.png');
noisy_img = imnoise(im2double(clean_img), 'gaussian', 0, 0.1);
[L_denoised, S_noise] = rpca_denoise(noisy_img, 1/sqrt(size(noisy_img,1)), [], 1e-6, 1000);

二、WNNM加权核范数去噪

function E = WNNM_DeNoising(N, O, Par)% WNNM去噪 输入:%   N - 含噪图像%   O - 干净图像 (参考)%   Par - 参数结构体% 输出:%   E - 去噪图像[m, n] = size(N);Par.lambda = 0.1;  % 稀疏惩罚参数Par.beta = 0.5;    % 核范数权重% 初始化E = N;Y = zeros(size(N));mu = 0.01;for k = 1:Par.max_iter% 更新E[U, S, V] = svd(E + Y/mu, 'econ');S = diag(S);S = max(S - Par.lambda/mu, 0);E = U * S * V';% 更新YY = Y + mu*(N - E);% 更新mumu = mu * 1.2;% 收敛判断if mod(k, 50) == 0fprintf('WNNM迭代 %d, 残差: %.2e\n', k, norm(N-E, 'fro'));endif mu > 1e5break;endend
end% 参数设置示例
Par.max_iter = 500;
Par.tol = 1e-6;
denoised_img = WNNM_DeNoising(noisy_img, clean_img, Par);

三、性能评估与可视化

% 计算指标
psnr_denoised = psnr(denoised_img, clean_img);
ssim_denoised = ssim(denoised_img, clean_img);% 显示结果
figure;
subplot(1,3,1); imshow(clean_img); title('原始图像');
subplot(1,3,2); imshow(noisy_img); title('含噪图像');
subplot(1,3,3); imshow(denoised_img); title('去噪结果');% 输出指标
fprintf('RPCA去噪效果:
PSNR=%.2f dB, SSIM=%.4f\n', psnr_denoised, ssim_denoised);

参考代码稀疏低秩去噪的MATLAB代码 www.youwenfan.com/contentcnr/65300.html