KSVD的稀疏编码去噪

KSVD（K-Singular Value Decomposition）是一种用于稀疏表示的字典学习算法，广泛应用于信号处理和图像处理中的去噪任务。

1. KSVD字典学习

function [D, X] = ksvd(Y, K, maxIter)% KSVD字典学习% 输入：%   Y - 输入信号矩阵 (每个列向量是一个信号)%   K - 字典原子的数量%   maxIter - 最大迭代次数% 输出：%   D - 学习到的字典%   X - 稀疏表示矩阵% 初始化字典[rows, cols] = size(Y);D = randn(rows, K);D = D ./ vecnorm(D);% 初始化稀疏表示矩阵X = zeros(K, cols);% KSVD迭代for iter = 1:maxIter% 稀疏编码for j = 1:colsresidual = Y(:, j);for k = 1:KX(k, j) = 0;if norm(residual) > 1e-6alpha = D(:, k)' * residual;X(k, j) = alpha;residual = residual - alpha * D(:, k);endendend% 字典更新for k = 1:K% 找到使用第k个原子的信号idx = find(X(k, :) ~= 0);if isempty(idx)continue;end% 更新第k个原子E = Y(:, idx) - D * X(:, idx);E = E + D(:, k) * X(k, idx);[U, S, V] = svd(E, 'econ');D(:, k) = U(:, 1);X(k, idx) = S(1, 1) * V(:, 1)';endend
end

2. 稀疏编码去噪

function denoised_signal = sparse_coding_denoising(noisy_signal, D, sparsity)% 稀疏编码去噪% 输入：%   noisy_signal - 含噪信号%   D - 学习到的字典%   sparsity - 稀疏度% 输出：%   denoised_signal - 去噪后的信号% 稀疏编码[rows, cols] = size(noisy_signal);X = zeros(size(D, 2), cols);for j = 1:colsresidual = noisy_signal(:, j);for k = 1:sparsity[~, idx] = max(abs(D' * residual));X(idx, j) = D(:, idx)' * residual;residual = residual - X(idx, j) * D(:, idx);endend% 重建信号denoised_signal = D * X;
end

3. 主函数

function ksvd_denoising_simulation()% KSVD稀疏编码去噪模拟主函数% 参数signal_length = 1024;sparsity = 5;maxIter = 100;K = 256; % 字典原子数量% 生成测试信号original_signal = randn(signal_length, 1);noisy_signal = original_signal + 0.1 * randn(signal_length, 1);% 学习字典[D, ~] = ksvd(noisy_signal, K, maxIter);% 稀疏编码去噪denoised_signal = sparse_coding_denoising(noisy_signal, D, sparsity);% 可视化结果figure;subplot(3, 1, 1);plot(original_signal);title('原始信号');xlabel('样本索引');ylabel('幅度');subplot(3, 1, 2);plot(noisy_signal);title('含噪信号');xlabel('样本索引');ylabel('幅度');subplot(3, 1, 3);plot(denoised_signal);title('去噪后的信号');xlabel('样本索引');ylabel('幅度');
end

参考代码 KSVD的稀疏编码去噪 www.youwenfan.com/contentcnm/98087.html

运行

运行ksvd_denoising_simulation()函数即可开始模拟。程序会生成测试信号，添加噪声，学习字典，进行稀疏编码去噪，并绘制原始信号、含噪信号和去噪后的信号。