A new nonconvex relaxation approach for low tubal rank tensor recovery

Abstract

In this paper, we consider the tensor recovery problem within the low tubal rank framework. A new nonconvex surrogate is proposed to approximate the tensor tubal rank. The main advantage is that it uses a class of nonconvex functions to penalize the singular tubes directly instead of penalizing the singular values as in existing methods. Our proposed surrogate can continuously approximate the tubal rank without breaking its composition structure and keep the intrinsic structural information of the tensor better than existing methods. We then develop an efficient iteratively reweighted tube thresholding algorithm to solve the tensor recovery model equipped with the new tubal rank surrogate and provide the theoretical guarantee for convergence. Simulation results on synthetical and practical data demonstrate the superior performance of the proposed method over several widely used methods in the literature.