Missing Elements Recovery Using Low-Rank Tensor Completion and Total Variation Minimization

Abstract

The Low-rank (LR) and total variation (TV) are two most popular regularizations for image processing problems and have sparked a tremendous number of researches, particularly for moving from scalar to vector, matrix or even high-order based functions. However, discretization schemes commonly used for TV regularization often ignore the difference of the intrinsic properties, which is not effective enough to exploit the local smoothness, let alone the problem of edge blurring. To address this issue, in this paper, we consider the color image as three-dimensional tensors, then measure the smoothness of these tensors by TV norm along the different dimensions. The three-order tensor is then recovered by Tucker decomposition factorization. Specifically, we propose integrating Shannon total variation (STV) into low-rank tensor completion (LRTC). Moreover, due to the suboptimality of nuclear norm, we propose a new nonconvex low-rank constraint for closer rank approximation, namely truncated $\gamma$-norm. We solve the cost function using the alternating direction method of multipliers (ADMM) method. Experiments on color image inpainting tasks demonstrate that the proposed method enhances the details of the recovered images.