压缩感知omp算法matlab代码
时间: 2023-10-09 19:12:02 浏览: 68
压缩感知OMP算法的Matlab代码如下:
```matlab
function [x] = OMP(A, y, K)
N = size(A, 2);
r = y;
omega = [];
for k = 1:K
proj = abs(A' * r);
[~, idx] = max(proj);
omega = [omega, idx];
x_omega = pinv(A(:, omega)) * y;
r = y - A(:, omega) * x_omega;
end
x = zeros(N, 1);
x(omega) = x_omega;
end
```
相关问题
图像压缩感知OMP重构算法Matlab代码
以下是一个基于稀疏表示和OMP(Orthogonal Matching Pursuit)算法的图像压缩感知重构算法的Matlab示例代码:
```matlab
% 读入图像
img = imread('example.jpg');
% 转换为灰度图像
img_gray = rgb2gray(img);
% 获取图像大小
[h, w] = size(img_gray);
% 构造稀疏基
Phi = dct2(eye(w)); % 离散余弦变换
% 生成测量矩阵
m = 3000;
Phi = Phi(randperm(w, m), :);
% 压缩图像
y = Phi * img_gray(:);
% OMP算法重构图像
n_iter = 50;
x = zeros(w, 1);
residual = y - Phi * x;
ind = [];
for i = 1:n_iter
proj = Phi' * residual;
[~, pos] = max(abs(proj));
ind = [ind, pos];
x(ind) = pinv(Phi(:, ind)) * y;
residual = y - Phi * x;
end
reconstructed_img = reshape(x, [h, w]);
% 显示原图像和重构图像
imshow(img_gray);
title('Original Image');
figure;
imshow(reconstructed_img, []);
title('Reconstructed Image');
```
该代码实现了一个基于稀疏表示和OMP算法的图像压缩感知重构算法,使用了离散余弦变换(DCT)作为稀疏基,利用随机矩阵生成测量矩阵,对图像进行压缩,并通过OMP算法重构图像。
生成matlab压缩感知omp算法代码
以下是使用Matlab编写的压缩感知OMP算法代码:
```matlab
function [x, residual] = omp(A, y, k)
%OMP Orthogonal Matching Pursuit
% [x, residual] = OMP(A, y, k) computes a k-sparse approximation of
% the solution of the linear system Ax = y, where A is a matrix of size
% mxn and y is a vector of length m. The algorithm terminates when the
% norm of the residual is less than a certain threshold. It returns the
% approximation x and the residual. The algorithm is based on the
% Orthogonal Matching Pursuit algorithm proposed in the paper
% "Matching Pursuits with Orthogonal Matching Pursuit" by Y. Pati,
% R. Rezaiifar and P. Krishnaprasad.
%
% INPUTS:
% A - mxn matrix
% y - m-dimensional vector
% k - sparsity level
%
% OUTPUTS:
% x - n-dimensional vector (k-sparse approximation of the solution of Ax=y)
% residual - m-dimensional vector (residual of the approximation)
[m, n] = size(A);
r = y;
x = zeros(n, 1);
omega = [];
for i = 1:k
max_value = 0;
max_index = 0;
for j = 1:n
if ~ismember(j, omega)
a = A(:, j);
value = abs(a' * r);
if value > max_value
max_value = value;
max_index = j;
end
end
end
omega = [omega max_index];
x(omega) = A(:, omega) \ y;
r = y - A(:, omega) * x(omega);
if norm(r) < 1e-6
break;
end
end
residual = r;
end
```
这是一个基本的OMP算法实现,使用了Matlab中的矩阵运算和控制语句。在输入矩阵A和向量y以及稀疏度k之后,该算法会计算出一个k稀疏的近似解x,并返回残差residual。