Laplace function based nonconvex surrogate for low-rank tensor completion

Abstract Recently, the tensor nuclear norm (TNN), which is the convex surrogate for tensor multi rank, has been successfully applied to the low-rank tensor completion (LRTC) problem. However, treating each singular value equally restricts the capability of TNN. In this work, we suggest the Laplace function based surrogate for tensor multi rank, which adaptively assigns weights to different singular values. We propose the corresponding surrogate based LRTC model and develop an efficient alternating direction method of multipliers (ADMM) to tackle the proposed model. Extensive experiments demonstrate that the proposed method outperforms state-of-the-art methods both quantitatively and qualitatively.