KSVD算法 matlab代码

以下是KSVD算法的MATLAB代码实现：

function [D,X,err] = ksvd(Y,D,X,param)
% Input:
% Y - Signal observation (m x n matrix)
% D - Initial dictionary (m x K matrix)
% X - Coefficient matrix (K x n matrix)
% param - Algorithm parameters structure
%
% Output:
% D - Learned dictionary (m x K matrix)
% X - Sparse coefficient matrix (K x n matrix)
% err - Error history (vector)

% Initialize error vector
err = zeros(param.max_iter,1);

% Loop over iterations
for i = 1:param.max_iter
    
    % Sparse coding
    X = omp(D'*Y, D'*D, param.sparsity);
    
    % Dictionary update
    for k = 1:param.K
        
        % Find samples that use atom k
        I = find(X(k,:));
        
        if ~isempty(I)
            
            % Compute error matrix
            E = Y(:,I) - D*X(:,I) + D(:,k)*X(k,I);
            
            % SVD of error matrix
            [U,S,V] = svds(E,1);
            
            % Update dictionary and coefficient matrix
            D(:,k) = U;
            X(k,I) = S*V';
        end
        
    end
    
    % Compute error
    err(i) = norm(Y - D*X,'fro')^2;
    
    % Check for convergence
    if i > 1 && abs(err(i) - err(i-1)) < param.tol
        break;
    end
    
end

end

function X = omp(Y, D, K)
% Solve OMP problem
% min ||x||_0 subject to y = D*x

[m,n] = size(Y);
X = zeros(size(D,2),n);

for i = 1:n
    
    % Initialize residual and index set
    r = Y(:,i);
    omega = [];
    
    % Loop over sparsity level
    for j = 1:K
        
        % Find index with largest projection
        [~,k] = max(abs(D'*r));
        
        % Add index to index set
        omega = [omega;k];
        
        % Solve least squares problem
        X(omega,i) = pinv(D(:,omega))*Y(:,i);
        
        % Update residual
        r = Y(:,i) - D(:,omega)*X(omega,i);
        
        % Check for convergence
        if norm(r) < 1e-6
            break;
        end
        
    end
    
end

end

其中，`param`是一个包含算法参数的结构体，具体内容如下：

param.K = 128; % Dictionary size
param.sparsity = 10; % Sparsity level
param.max_iter = 50; % Maximum number of iterations
param.tol = 1e-6; % Convergence tolerance

使用方法如下：

% Load signal data
load('signal_data.mat');

% Set algorithm parameters
param.K = 128;
param.sparsity = 10;
param.max_iter = 50;
param.tol = 1e-6;

% Initialize dictionary and coefficient matrix
D = randn(size(Y,1),param.K);
X = zeros(param.K,size(Y,2));

% Run KSVD algorithm
[D,X,err] = ksvd(Y,D,X,param);