Enhanced nonconvex low-rank representation for tensor completion

Higher-order low-rank tensor arises in many data processing applications and has attracted great interests. In this paper, we propose a new low rank model for higher-order tensor completion task based on the double nonconvex $L_{\gamma}$ norm, which is used to better approximate the rank minimization of tensor mode-matrix. An block successive upper-bound minimization method-based algorithm is designed to efficiently solve the proposed model, and it can be demonstrated that our numerical scheme converge to the coordinatewise minimizers. Numerical results on three types of public multi-dimensional datasets have tested and shown that our algorithms can recover a variety of low-rank tensors with significantly fewer samples than the compared methods.