Robust Generalized Low-Rank Decomposition of Multimatrices for Image Recovery

Abstract

Low-rank approximation has been successfully used for dimensionality reduction, image noise removal, and image restoration. In existing work, input images are often reshaped to a matrix of vectors before low-rank decomposition. It has been observed that this procedure will destroy the inherent two-dimensional correlation within images. To address this issue, the generalized low-rank approximation of matrices (GLRAM) method has been recently developed, which is able to perform low-rank decomposition of multiple matrices directly without the need for vector reshaping. In this paper, we propose a new robust generalized low-rank matrices decomposition method, which further extends the existing GLRAM method by incorporating rank minimization into the decomposition process. Specifically, our method aims to minimize the sum of nuclear norms and $l_{1}$ -norms. We develop a new optimization method, called alternating direction matrices tri-factorization method , to solve the minimization problem. We mathematically prove the convergence of the proposed algorithm. Our extensive experimental results demonstrate that our method significantly outperforms existing GLRAM methods.