Low-rank tensor completion based on tensor train rank with partially overlapped sub-blocks

Abstract

Recently, low-rank tensor based methods using tensor train (TT) rank have achieved promising performance on multidimensional signal processing. Especially taking advantage of a tensor augmentation technique called ket augmentation (KA), methods based on TT rank can more efficiently capture correlation of the generated higher-order tensor, but serious block artifacts are caused. In this paper, a tensor completion method using parallel matrix factorization based on TT rank with partially overlapped sub-blocks is proposed. Combined with the partially overlapped sub-blocks scheme and KA technique, an improved tensor augmentation technique is proposed to further increase the order of generated tensor, enhance the low-rankness, and alleviate block artifacts. To reduce the computational time, parallel matrix factorization is utilized to minimize the TT rank. Besides, a fixed weighting function is also developed to reduce the blockiness effect according to the shortest distance between the pixel and the corresponding sub-block boundaries. Numerical experiments demonstrate the superiority of the proposed method over the existing state-of-the-art methods in terms of quality and quantity.