A novel non-convex minimax $p$-th order concave penalty function approach to low-rank tensor completion

• URL: http://arxiv.org/abs/2502.19979v2
• Date: Fri, 06 Jun 2025 16:43:00 GMT
• Title: A novel non-convex minimax $p$-th order concave penalty function approach to low-rank tensor completion
• Authors: Hongbing Zhang, Bing Zheng,
• Abstract summary: The low-rank tensor completion (LRTC) problem aims to reconstruct a tensor from partial sample information.<n>To address this performance, a novel minimax $p$-th order penalty (MPCP) is proposed.<n>The proposed model outperforms the state-of-the-art datasets in both visual quality and quantitative metrics.
• Score: 10.75561026701747
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The low-rank tensor completion (LRTC) problem aims to reconstruct a tensor from partial sample information, which has attracted significant interest in a wide range of practical applications such as image processing and computer vision. Among the various techniques employed for the LRTC problem, non-convex relaxation methods have been widely studied for their effectiveness in handling tensor singular values, which are crucial for accurate tensor recovery. While the minimax concave penalty (MCP) non-convex relaxation method has achieved promising results in tackling the LRTC problem and gained widely adopted, it exhibits a notable limitation: insufficient penalty on small singular values during the singular value handling process, resulting in inefficient tensor recovery. To address this issue and enhance recovery performance, a novel minimax $p$-th order concave penalty (MPCP) function is proposed. Based on this novel function, a tensor $p$-th order $\tau$ norm is proposed as a non-convex relaxation for tensor rank approximation, thereby establishing an MPCP-based LRTC model. Furthermore, theoretical convergence guarantees are rigorously established for the proposed method. Extensive numerical experiments conducted on multiple real datasets demonstrate that the proposed method outperforms the state-of-the-art methods in both visual quality and quantitative metrics.

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