Improvement of robust tensor principal component analysis based on generalized nonconvex approach

The problem of nonconvex robust tensor principal component analysis consists of recovering the low-rank and sparse part from a tensor corrupted by noise, which attracts a great deal of attention in a wide range of practical situations. However, existing nonconvex methods face a number of problems, the two most important of which are the restrictions on specific nonconvex functions and the information loss in low-rank part. In this paper, we propose a generalized nonconvex robust tensor principal component analysis model that includes some of the most popular nonconvex functions. Furthermore, we propose a partial weighted tensor nuclear norm and the corresponding partial weighted singular value thresholding operator to improve the generalized model, further reducing the loss of underlying tensor information while recovering the low rank tensor. Besides, two ADMM-based nonconvex algorithms are proposed to the generalized nonconvex model and the improved model respectively. We also analyze the convergence of the algorithms, the computational complexity, and the theoretical guarantee of the proposed models. Numerical experimental results on image data and video data show that our proposed models has superior performance compared to several state-of-the-art methods.