matlab omp算法代码
时间: 2023-09-08 17:09:21 浏览: 51
以下是 MATLAB 中 OMP 算法的示例代码:
```matlab
function [x, res] = omp(A, b, k)
% OMP Algorithm for sparse signal recovery
% A: Sensing matrix (m x n)
% b: Measurement vector (m x 1)
% k: Sparsity level of the signal
[m, n] = size(A);
x = zeros(n, 1);
res = b; % Initialize residual
for i = 1:k
% Compute inner products between residual and columns of A
inner_products = abs(A' * res);
[~, index] = max(inner_products);
% Add selected index to support
support(i) = index;
% Solve least-squares problem on support
x(support(1:i)) = A(:, support(1:i)) \ b;
% Update residual
res = b - A * x;
end
end
```
使用方法:
```matlab
% Generate random sensing matrix and sparse signal
m = 50;
n = 100;
k = 10;
A = randn(m, n);
x_true = zeros(n, 1);
support = randperm(n, k);
x_true(support) = randn(k, 1);
% Generate measurements
b = A * x_true;
% Run OMP algorithm
[x, res] = omp(A, b, k);
% Plot results
figure;
subplot(2, 1, 1);
stem(x_true, 'LineWidth', 1.5);
hold on;
stem(x, 'LineWidth', 1.5);
xlabel('Index');
ylabel('Value');
legend('True signal', 'Recovered signal');
title('Sparse signal recovery using OMP');
subplot(2, 1, 2);
plot(res, 'LineWidth', 1.5);
xlabel('Iteration');
ylabel('Residual');
title('Convergence of OMP algorithm');
```
此代码将生成一个随机的测量矩阵和稀疏信号,并使用 OMP 算法来恢复信号。最终将绘制原始信号、恢复信号和残差的图形。