Stable Principal Component Pursuit via Convex Analysis

This paper aims to recover a low-rank matrix and a sparse matrix from their superposition observed in additive white Gaussian noise by formulating a convex optimization problem with a non-separable non-convex regularization. The proposed non-convex penalty function extends the recent work of a multivariate generalized minimax-concave penalty for promoting sparsity. It avoids underestimation characteristic of convex regularization, which is weighted sum of nuclear norm and l(1) norm in our case. Due to the availability of convex-preserving strategy, the cost function can he minimized through forward-backward splitting. The performance of the proposed method is illustrated for both numerical simulation and hyperspectral images restoration.