Tensor recovery based on Bivariate Equivalent Minimax-Concave Penalty

Abstract

In tensor recovery problem, larger singular values often correspond to the primary information of the image, such as contours, sharp edges and smooth areas. The minimum–maximum concave penalty (MCP) function has been effective in preserving larger singular values and achieving good tensor recovery results. However, in the process of solving this problem, singular values may vary during iterations, and the fixed parameters of the MCP function may not sufficiently preserve all the larger singular values, which may hinder the attainment of optimal results in tensor recovery. To overcome this challenge, we propose the Bivariate Equivalent Minimax-Concave Penalty (BEMCP) theorem, which allows the parameters to adapt to the changes in singular values and more comprehensively preserve the larger singular values. For low-rank tensor completion and tensor robust principal component analysis problems, we propose BEMCP-based models. Finally, experiments with various real-world data demonstrate that the proposed methods outperform state-of-the-art methods.