Iterative Adaptive Nonconvex Low-Rank Tensor Approximation to Image Restoration Based on ADMM

In this paper, in order to recover more finer details of the image and to avoid the loss of image structure information for image restoration problem, we develop an iterative adaptive weighted core tensor thresholding (IAWCTT) approach based on the alternating direction method of multipliers (ADMM). By observing the decoupling property of the ADMM algorithm, we first propose that the key step to image restoration is to tackle the denoising subproblem efficiently using appropriate prior information. Secondly, by analyzing the properties of the core tensor, we propose that low-rank tensor approximation can be implemented by penalizing the core tensor itself, instead of penalizing the CP rank, Tucker rank or the multilinear rank and Tubal rank. The IAWCTT approach is proposed to solve the denoising subproblem in the ADMM framework, and we claim that such an adaptive weighted scheme is equivalent to a kind of nonconvex penalty for the core tensor; thus, it is unnecessary to use the nonconvex penalty term to induce strong sparse/low-rank solution in image restoration optimization problem, because the scheme that selecting appropriate weights to the convex penalty term can also lead to strong sparse/low-rank solution. Numerical experiments show that our proposed model and algorithm are comparable to other state-of-the-art models and methods.