【图像重建】基于ADMM的tv正则化最小化稀疏实现图像重建附matlab代码

本文链接：https://blog.youkuaiyun.com/matlab_dingdang/article/details/124811055

该博客演示了一个使用TVAL3算法进行图像恢复的MATLAB简单示例。首先创建了一个64x64的幻影图像，然后通过随机矩阵进行观测并添加噪声。之后，利用TVAL3算法进行图像重构，并展示了重构后的结果。文章还引用了相关文献，探讨了L1与TV正则化的图像重建方法。

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1 简介

2 部分代码

% This simple demo examines if TVAL3 works normally. Please try more demos% in the "Demos" directory, which would show users what TVAL3 is capable of.% % I: 64x64 phantom (real, two-dimentional)% A: random matrix without normality and orthogonality (real)% f: observation with/without noise (real)%clear; close all;path(path,genpath(pwd));fullscreen = get(0,'ScreenSize');% problem sizen = 64;ratio = .21;p = n; q = n; % p x q is the size of imagem = round(ratio*n^2);% sensing matrixA = rand(m,p*q)-.5;% original imageI = phantom(n);nrmI = norm(I,'fro');figure('Name','TVAL3','Position',...    [fullscreen(1) fullscreen(2) fullscreen(3) fullscreen(4)]);subplot(121); imshow(I,[]);title('Original phantom','fontsize',18); drawnow;% observationf = A*I(:);favg = mean(abs(f));% add noisef = f + .00*favg*randn(m,1);%% Run TVAL3clear optsopts.mu = 2^8;opts.beta = 2^5;opts.tol = 1E-3;opts.maxit = 300;opts.TVnorm = 1;opts.nonneg = false;opts.disp = false;opts.TVL2 = false;t = cputime;[U, out] = TVAL3(A,f,p,q,opts);t = cputime - t;subplot(122); imshow(U,[]);title('Recovered by TVAL3','fontsize',18);xlabel(sprintf(' %2d%% measurements \n Rel-Err: %4.2f%%, CPU: %4.2fs ',ratio*100,norm(U-I,'fro')/nrmI*100,t),'fontsize',16);