Manifold constrained joint sparse learning via non-convex regularization

Abstract The traditional robust principal component analysis (RPCA) via decomposition into low-rank plus sparse matrices offers a powerful framework for a large variety of applications in computer vision. However, the reconstructed image experiences serious interference by Gaussian noise, resulting in the degradation of image quality during the denoising process. Thus, a novel manifold constrained joint sparse learning (MCJSL) via non-convex regularization approach is proposed in this paper. Morelly, the manifold constraint is adopted to preserve the local geometric structures and the non-convex joint sparsity is introduced to capture the global row-wise sparse structures. To solve MCJSL, an efficient optimization algorithm using the manifold alternating direction method of multipliers (MADMM) is designed with closed-form solutions and it achieves a fast and convergent procedure. Moreover, the convergence is analyzed mathematically and numerically. Comparisons among the proposed MCJSL and some state-of-the-art solvers, on several accessible datasets, are presented to demonstrate its superiority in image denoising and background subtraction. The results indicate the importance to incorporate the manifold learning and non-convex joint sparse regularization into a general RPCA framework.