RPCA图像处理中的矩阵重建算法及其应用

%MATLAB code，子函数
function [A_hat E_hat ] =rpca(res)
%res:输入图像;输出为低秩A_hat和稀疏E_hat
% Copyright (C) 2016,4, all rights reserved.
 [row col] = size(res);
    lambda = 1/ sqrt(max(size(res)));%
    tol = 1e-7;
    maxIter = 1000;
% initialize
Y = res;
[u,s,v]=svd(Y);
norm_two=s(1);
norm_inf=max(abs(Y(:)))/lambda;
dual_norm = max(norm_two, norm_inf);
Y = Y / dual_norm;


A_hat = zeros( row, col);
E_hat = zeros( row, col);
mu = 0.01/norm_two; % this one can be tuned
mu_bar = mu * 1e7;
rho = 1.9  ;       % this one can be tuned
d_norm=sqrt(sum(res(:).^2));
iter = 0;
total_svd = 0;
converged = 0;%收敛
stopCriterion = 1;
sv = 10;
while ~converged
    iter = iter + 1;
    temp_T = res - A_hat + (1/mu)*Y;
    E_hat=temp_T - lambda/mu;
    n1=find(E_hat<0);
    E_hat(n1)=0;
    
    tmp=temp_T + lambda/mu;
    n1=find(tmp>0);
    tmp(n1)=0;
    E_hat= E_hat+tmp;
    
    [U1 S1 V1] = svd(res - E_hat + (1/mu)*Y);
   if  chsvd(col, sv) == 1
            U=U1(:,1:sv);
            S=S1(:,1:sv);
            V=V1(:,1:sv);
     end   
     
    diagS = diag(S);
    svp = length(find(diagS > 1/mu));
    if svp < sv
        sv = min(svp + 1, col);
    else
        sv = min(svp + round(0.05*col), col);
    end


%     A_hat = U(:, 1:svp) * diag(diagS(1:svp) - 1/mu) * V(:, 1:svp)';
    U2=U(:, 1:svp);
    S2=diag(diagS(1:svp) - 1/mu);
    V2=V(:, 1:svp)';
    A_hat=U2*S2*V2;
    total_svd = total_svd + 1;
    
    Z = res - A_hat - E_hat;
    
    Y = Y + mu*Z;
    mu = min(mu*rho, mu_bar);
    
    %% stop Criterion
    stopCriterion = sqrt(sum(Z(:).^2)) / d_norm;
    if stopCriterion < tol
        converged = 1;
    end
    if ~converged && iter >= maxIter
        disp('Maximum iterations reached') ;
        converged = 1 ;
    end
end
end
function y=chsvd( n, d)
     y=0;
if ((n<=100)&&(d/n<=0.02)) y=1;end
         if((n<=200)&&(d/n<=0.06)) y=1; end
if((n<=300)&&(d/n<=0.26)) y=1;end
if((n<=400)&&(d/n<=0.28)) y=1;end
if((n<=500)&&(d/n<=0.34)) y=1;end
if(n>500&&(d/n<=0.38)) y=1;end
end