Projected Entangled Pair State Tensor Network for Colour Image and Video Completion

Abstract

Tensor decompositions, such as the CP, Tucker, tensor train, and tensor ring decomposition, have yielded many promising results in science and engineering. However, a more general tensor model known as the projected entangled pair state (PEPS) tensor network has not been widely considered for colour image and video processing, although it has long been studied in quantum physics. In this study, we constructed the relationship between the generalized tensor unfolding matrices and the PEPS ranks. Furthermore, we employed the PEPS tensor network for the high-order tensor completion problem and developed an efficient gradient-based optimisation algorithm to find the latent factors of the incomplete tensor, which we used to fill the missing entries of the tensor. Comparing the proposed method with state-of-the-art methods, experimental results for colour image and video completion confirm the effectiveness of the proposed methods.