Robust principal component analysis based on low-rank and block-sparse matrix decomposition

In this paper, we propose a convex program for low-rank and block-sparse matrix decomposition. Potential applications include outlier detection when certain columns of the data matrix are outliers. We design an algorithm based on the augmented Lagrange multiplier method to solve the convex program. We solve the subproblems involved in the augmented Lagrange multiplier method using the Douglas/Peaceman-Rachford (DR) monotone operator splitting method. Numerical simulations demonstrate the accuracy of our method compared with the robust principal component analysis based on low-rank and sparse matrix decomposition.