Robust Schattenp Norm Based Approach for Tensor Completion The matrix nuclear norm has been widely applied to approximate the matrix rank for lowrank tensor completion because of its convexity. However, this relaxation may make the solution seriously deviate from the original solution for realworld data recovery. In this paper, using a nonconvex approximation of rank, i.e., the Schattenp norm, we propose a novel model for tensor completion. Itxe2x80x99s hard to solve this model directly because the objective function of the model is nonconvex. To solve the model, we develop a variant of this model via the classical quadric penalty method, and propose an algorithm, i.e., SpBCD, based on the block coordinate descent method. Although the objective function of the variant is nonconvex, we show that the sequence generated by SpBCD is convergent to a critical point. Our numerical experiments on realworld data show that SpBCD delivers stateofart performance in recovering missing data.

Tensor Completion via Global LowTubalRankness and Nonlocal SelfSimilarity The recent popular tensor nuclear norm (TNN), a convex surrogate of tensor tubal rank, obtains promising results in tensor completion. Although the TNNbased model has shown its prominent capability of characterizing the global structure of tensors, it lacks the capability for preserving the abundant details of the target tensor. By integrating the global lowtubalrankness and nonlocal selfsimilarity, we propose a novel tensor completion model, which recovers the global structural information by TNN regularizer while compensating for the details by plugging in a denoiser to express the nonlocal selfsimilarity prior. We design an alternating directional method of multipliers (ADMM)based algorithm to solve the proposed model. Extensive experimental results on color images and fluorescence microscope images demonstrate the superiority of the proposed method over the compared ones.