Nonconvex Robust Quaternion Matrix Completion for Imaging Processing

2024/10/19 by Baohua Huang, Huang, Baohua, Jiakai Chen +3
Computer Science · Engineering · #Digital Image Processing Techniques #FOS: Mathematics #Medical Image Segmentation Techniques #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.2410.15006

openalex publication_date 2024/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

One of the tasks in color image processing and computer vision is to recover clean data from partial observations corrupted by noise. To this end, robust quaternion matrix completion (QMC) has recently attracted more attention and shown its effectiveness, whose convex relaxation is to minimize the quaternion nuclear norm plus the quaternion L₁-norm. However, there is still room to improve due to the convexity of the convex surrogates. This paper proposes a new nonconvex robust QMC model, in which the nonconvex MCP function and the quaternion L_p-norm are used to enhance the low-rankness and sparseness of the low-rank term and sparse term, respectively. An alternating direction method of multipliers (ADMM) algorithm is developed to solve the proposed model and its convergence is given. Moreover, a novel nonlocal-self-similarity-based nonconvex robust quaternion completion method is proposed to handle large-scale data. Numerical results on color images and videos indicate the advantages of the proposed method over some existing ones.

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