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 ℓ₁ norm in our case. Due to the availability of convex-preserving strategy, the cost function can be minimized through forward-backward splitting. The performance of the proposed method is illustrated for both numerical simulation and hyperspectral images restoration.