Low-Rank tensor completion based on nonconvex regularization

Abstract

In this paper, we consider the low-rank tensor completion which aims to exactly recover incomplete high-dimensional visual data. Existing studies utilize widely tensor nuclear norm minimization (TNNM), a convex relaxation to tensor-rank minimization (TRM), to solve tensor completion tasks. Nevertheless, TNNM ignores the difference between different tensor singular values induced by the tensor singular value decompositions (t-SVD) and then the obtained solution may be suboptimal. In this paper, we propose a nonconvex minimization approach to solve the tensor completion problem more effectively by adopting a nonconvex regularization to further approximate the tensor-rank. Moreover, alternating direction method of multipliers (ADMM) and iteratively reweighted nuclear norm (IRNN) are adopted to solve the constructed nonconvex models efficiently, and the convergence can also be guaranteed. Finally, we present that the proposed nonconvex optimization methods are suitable for solving other TRM problems induced by any invertible linear transform, such as subspace clustering based on low-rank representation. Extensive experiments on real images and videos validate the superiority of our approach over the state-of-the-art algorithms.