Robust Principal Component Analysis

Solver to solve the Robust Principal Component Analysis (RPCA) via ADMM

RPCA Image Inpainting/RPCA_ADMM.m

@@ -39,14 +39,14 @@
 
  % L subproblem
  X = M + Mu./rho;
- L = svt(X - S , 1/rho); %Solve for L, by singular value thresholding
+ L = svt(X-S , 1/rho); %Solve for L, by singular value thresholding
 
  % S subproblem
- S = shrink(X - L, lam/rho); %Solve for S by soft thresholding
+ S = shrink(X-L, lam/rho); %Solve for S by soft thresholding
 
- Mu = Mu + rho*(M - L - S); %Update our Lagrange multipliers
+ Mu = Mu - rho*(L+S-M); %Update our Lagrange multipliers
 
- E_r = M - L - S;
+ E_r = L+S-M;
 
  relError(i) = norm(E_r,'fro')/norm(M, 'fro');
 

RPCA Image Inpainting/RPCA_Demo.m

@@ -2,7 +2,8 @@
 clear all;
 close all;
 
-% Created on 3/07/2017 by Tarmizi Adam
+% First Created on 3/07/2017 by Tarmizi Adam
+% Update History : 8/6/2019,
 % Demo for robust principal component analysis (RPCA) using ADMM
 % Uses the ADMM/ADM algorithm to solve the the pricipal component pursuit:
 %
@@ -16,13 +17,13 @@
 
 Img = imread('peppers.bmp');
 
-sigma = 0.1;
+sigma = 0.2; %density of the noise
 Img_n = imnoise(Img,'salt & pepper',sigma);
 Img_n = double(Img_n);
 
 %% ==================== Parameter options =====================
 
-opts.lam = 0.068; % Regularization parameter
+opts.lam = 0.053; % Regularization parameter
 opts.Nit = 1000; % Algorithm iteration
 opts.tol = 1.0e-5; %Stopping criterion value
 opts.rho = 0.05; % Regularization param of ADMM constraint