Schatten Capped p Regularization for Robust Principle Component Analysis

Robust Principal Component Analysis (RPCA) is widely used for low-rank matrix recovery, which restores low-rank structures in damaged data through matrix decomposition. Existing approaches adopt the nuclear norm as a convex approximation of rank function. However, the nuclear norm treats the different singular values equally, leading to suboptimal matrix representation. To better depict the low-rank part, in this paper, we adopt a better surrogate of rank function, namely Schatten Capped p regularization. Further, the Schatten Capped p regularization-based RPCA model is proposed. And then we propose an efficient Alternating Direction Method of Multiplier (ADMM) algorithm to solve for the resulting optimization model. Experimentally, our algorithm is compared to state-of-the-art methods in practical applications such as image denoising, video background and foreground separation, and face de-shadowing. Especially, our algorithm can separate the noise better than other algorithms in the case of low noise levels in image denoising.