Fast cross tensor approximation for image and video completion

Abstract

This paper presents a framework that suggests the utilization of cross tensor approximation or tensor CUR approximation to reconstruct incomplete images and videos. The proposed algorithms are significant due to their simple implementation and low computational complexity. We further suggest the use of efficient smooth tensor CUR algorithms for data tensors with structural missing components or high missing rates. These algorithms make the sampled fibers smoother and subsequently apply the proposed CUR algorithms. Our numerical experiments exhibit that this smoothing process provides significant benefits. The primary contribution of this paper is to design and examine enhanced multistage CUR algorithms with smoothing pre-processing for the tensor completion problem. The secondary contribution includes a thorough analysis of the efficiency of image reconstruction using four distinct CUR strategies via comprehensive computer simulations. Our simulations showed clearly that the suggested algorithms perform comparably to, and frequently even better than, the majority of the current state-of-the-art methods developed for the tensor completion problem while at the same time they are much faster. Additionally, we offer the MATLAB codes on GitHub for use in a variety of applications. To the best of our knowledge, no research or comparisons of CUR (cross approximation) algorithms for image and video completion have been done to date.