Low rank matrix recovery from sparse noise by ℓ2,1 loss function

In the last decades, Robust Principal Component Analysis (PCA) has been drawn much attention in the image processing, computer vision and machine learning communities and various robust PCA methods have been developed. This paper introduces a new generalized robust PCA with emphasizing on ℓ2, 1-norm minimization on loss function. The ℓ2, 1-norm instead of Frobenius norms based loss function is robust to outliers in data points. An efficient algorithm combine augmented Lagrange multiplier is develops. The experiments on both numerical simulated data and benchmark picture demonstrate that the proposed method outperforms the state-of-the-art because our method needs less iteration and more robust to outliers in data points.