Robust PCA via non-convex half-quadratic regularization

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, indicating 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 coordinate 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 parameter 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.