RPCA (robust PCA), low-rank sparse decomposition

MATLAB code, sub-function

function [A_hat e_hat] =RPCA (res)%res, input image, output is low rank a_hat and sparse e_hat [row col] = size (res);    Lambda = 1/sqrt (max (Size (res)));    Tol = 1e-7; Maxiter = 1000;% Initializey = 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 Tunedmu_bar = mu * 1e7;rho = 1.9;  % this one can be tunedd_norm=sqrt (sum (res (:). ^2)); iter = 0;TOTAL_SVD = 0;converged = 0;% Convergence 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);    Percent 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; Endendendfunction 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;endend

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RPCA (robust PCA), low-rank sparse decomposition