Image completion with approximate convex hull tensor decomposition

Abstract

Many image completion methods are based on a low-rank approximation of the underlying image using matrix or tensor decomposition models. In this study, we assume that the image to be completed is represented by a multi-way array and can be approximated by a conical hull of subtensors in the observation space. If an observed tensor is near-separable along at least one mode, the extreme rays, represented by the selected subtensors, can be found by analyzing the corresponding convex hull. Following this assumption, we propose a geometric algorithm to address a low-rank image completion problem. The extreme rays are extracted with a segmented convex-hull algorithm that is suitable for performing noise-resistant non-negative tensor factorization. The coefficients of a conical combination of such rays are estimated using Douglas–Rachford splitting combined with the rank-two update least-squares algorithm. The proposed algorithm was applied to incomplete RGB images and a hyperspectral 3D array with a large number of randomly missing entries. Experiments confirm its good performance with respect to other well-known image completion methods.