Image Completion with Filtered Low-Rank Tensor Train Approximations

Abstract

The topic of image completion has received increasing attention in recent years, motivated by many important applications in computer vision, data mining and image processing. In this study, we consider the problem of recovering missing values of pixels in highly incomplete images with a random or irregular structure. The analyzed gray-scale or colour images are transformed to multi-way arrays which are then recursively approximated by low-rank tensor decomposition models. In our approach, the multi-way array is represented by the tensor train model, and in each iterative step, the low-rank approximation is filtered with the Gaussian low-pass filter. As a result, the proposed algorithms considerably outperform the state-of-the art methods for matrix and tensor completion problems, especially when an incompleteness degree is very high, e.g. with 90% of missing pixels.