One-bit tensor completion via transformed tensor singular value decomposition

Abstract

This paper considers the problem of low-tubal-rank tensor completion from incomplete one-bit observations. Our work is inspired by the recently proposed invertible linear transforms based tensor-tensor product and transformed tensor singular value decomposition (t-SVD). Under this framework, a tensor nuclear norm constrained maximum log-likelihood estimation model is proposed, which is convex and efficiently solved. The feasibility of the model is proved with an upper bound of the estimation error obtained. We also show a lower bound of the worst-case estimation error, which combing with the obtained upper bound demonstrates that the estimation error is nearly order-optimal. Furthermore, an algorithm based on the alternating direction multipliers method (ADMM) and non-monotone spectral projected-gradient (SPG) method is designed to solve the estimation model. Simulations are performed to show the effectiveness of the proposed method, and the applications to real-world data demonstrate the promising performance of the proposed method.