One-bit tensor completion via transformed tensor singular value decomposition

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 trans -forms 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 up-per 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 pro-posed method. (c) 2021 Elsevier Inc. All rights reserved.

Automated summary

This paper proposes a maximum log-likelihood estimation model based on tensor nuclear norm constraint, proving the feasibility of the model by obtaining an upper bound of the estimation error, demonstrating that the estimation error is nearly order-optimal, and designing an algorithm for solving the estimation model.