Iterative p-shrinkage thresholding algorithm for low Tucker rank tensor recovery

Abstract

Low-rank tensor recovery, as a higher order extension of low-rank matrix recovery, has generated a great deal of research interests in recent years, such as image inpainting, video inpainting, video decoding, scan completion, and so on. In this paper, we propose an easy-to-implement algorithm based on the framework of alternative direction method, named iterative p-shrinkage thresholding algorithm, for solving the low Tucker rank tensor recovery problem. The performance of the proposed algorithm is investigated on both synthetic and real data. Numerical results on simulation data demonstrate that our algorithm can successfully recover varieties of synthetic low Tucker rank tensors in different sampling ratios with better quality compared to the existing state-of-the-art tensor recovery algorithms. Experiments on real data, including colored image inpainting, MRI image inpainting and hyperspectral image inpainting, further illustrate the effectiveness of the proposed iterative p-shrinkage thresholding algorithm.