Image Inpainting Exploiting Tensor Train and Total Variation

In this paper, we propose a novel approach to RGB image inpainting, which recovers missing entries of image by using low rank tensor completion. The approach is based on recently proposed tensor train (TT) decomposition, which is used to effectively enforce the low rankness of the image. In addition, our approach exploits the local smooth priors of visual data by incorporating the 2D total variation. Ket augmentation (KA) scheme is used to permute the image to a high order tensor, and then low rankness of balanced KA-TT matrices and total variation (TV) norm constraints are applied to recover the missing entries of the image. In order to reduce the computational complexity, in the proposed approach, nuclear norm is replaced by minimum Frobenius norm of two factorization matrices, which reduces the time for singular value decomposition (SVD). Lastly, in order to solve the proposed model, the efficient alternating direction method of multipliers (ADMM) is developed. The results of image inpainting experiments demonstrate the significantly superior performance of our approach.