Nonconvex Tensor Relative Total Variation for Image Completion

Image completion, which falls to a special type of inverse problems, is an important but challenging task. The difficulties lie in that (i) the datasets usually appear to be multi-dimensional; (ii) the unavailable or corrupted data entries are randomly distributed. Recently, low-rank priors have gained importance in matrix completion problems and signal separation; however, due to the complexity of multi-dimensional data, using a low-rank prior by itself is often insufficient to achieve desirable completion, which requires a more comprehensive approach. In this paper, different from current available approaches, we develop a new approach, called relative total variation (TRTV), under the tensor framework, to effectively integrate the local and global image information for data processing. Based on our proposed framework, a completion model embedded with TRTV and tensor p-shrinkage nuclear norm minimization with suitable regularization is established. An alternating direction method of multiplier (ADMM)-based algorithm under our framework is presented. Extensive experiments in terms of denoising and completion tasks demonstrate our proposed method are not only effective but also superior to existing approaches in the literature.