Robust Matrix Completion Method Based on TNNR and Total Row Difference for Recovering Optical Image

Abstract

Matrix completion aims to recover a matrix from an incomplete matrix with many unknown elements and has wide applications in optical image recovery and machine learning, in which the popular method is to formulate it as a general low-rank matrix approximation problem. However, the traditional optimization model for matrix completion is less robust. This article proposes a robust matrix completion method in which the truncated nuclear norm regularization (TNNR) is used as the approximation of the rank function and the sum of absolute values of the row difference, which is called the total row difference, is used to constrain the oscillations of the missing matrix. By minimizing the value of the total row difference in the objective, the proposed model controls the oscillation and reduces the impact of missing parts in the process of matrix completion continuously. Furthermore, we propose a two-step iterative algorithm framework and design an ADMM algorithm for the subproblem model that includes minimizing the total row difference. Experiments show that the proposed algorithm has more stable performance and better recovery effect and obviously reduces the sensitivity of the traditional TNNR models to the truncated rank parameter.