Robust PCA via non-convex half-quadratic regularization

作者：Wang, Zhi-Yong; Li, Xiao Peng^*; So, Hing Cheung; Liu, Zhaofeng

来源：SIGNAL PROCESSING, 2023, 204: 108816.

DOI：10.1016/j.sigpro.2022.108816

• Robust PCA
• Matrix factorization
• Low-rank
• Sparse
• Non-convex regularization
• Proximal block coordinate descent

In this paper, we propose a new non-convex regularization term named half-quadratic function to achieve robustness and sparseness for robust principal component analysis, and derive its proximity operator, in-dicating that the resultant optimization problem can be solved in computationally attractive manner. In addition, the low-rank matrix component is expressed as the factorization form and proximal block co-ordinate descent is leveraged to seek its solution, whose convergence is rigorously analyzed. We prove that any limit point of the iterations is a critical point of the objective function. Furthermore, the param-eter that controls the robustness and sparseness in our algorithm, is automatically adjusted according to the statistical residual error. Experimental results based on synthetic and real-world data demonstrate that the devised algorithm can effectively extract the low-rank and sparse components. MATLAB code is available at https://github.com/bestzywang .