Anisotropic Total Variation Regularized Low-Rank Tensor Completion Based On Tensor Nuclear Norm for Color Image Inpainting

Abstract

In this paper, we propose a novel low-rank tensor completion (LRTC) model under the circulant algebra for color image inpainting, which simultaneously preserves the low-rank structures of images, and also explore the local smooth and piecewise priors of the images in the spatial domain. First, color images are naturally represented by 3-order tensors which preserve the intrinsic structures of color images. Second, we preserve the low-rank structures of these tensors with tensor nuclear norm, which can simultaneously exploit the correlations among the spatial and channel domains. Third, we integrate an anisotropic total variation into our low-rank tensor completion model, which preserve the local smooth and piecewise priors of color images. Then, an efficient alternating direction method of multipliers (ADMM) is proposed to solve the resulting optimization problem. Experimental results on eight widely used color images demonstrate the effectiveness and superiority of the proposed algorithm.