A Weighted Tensor Factorization Method for Low-rank Tensor Completion

Recently, low-rank tensor completion has attracted increasing attention in recovering incomplete tensor whose elements are missing. The basic assumption is that the underlying tensor is a low-rank tensor, and therefore tensor nuclear norm minimization can be applied to recover such tensor. By taking color images as third-order tensors, it has been shown that these tensors are not necessary to be low-rank. The main aim of this paper is to propose and develop a weighted tensor factorization method for low-rank tensor completion. The main idea is to determine a suitable weight tensor such that the multiplication of the weight tensor to the underlying tensor can be low-rank or can be factorized into a product of low-rank tensors. Fast iterative minimization method can be designed to solve for the weight tensor and the underlying tensor very efficiently. We make use of color images as examples to illustrate the proposed approach. A series of experiments are conducted on various incomplete color images to demonstrate the superiority of our proposed low-rank tensor factorization method by comparing with the state-of-the-art methods in color image completion performance.