Robust and Parallelizable Tensor Completion Based on Tensor Factorization and Maximum Correntropy Criterion

Abstract

Robust tensor completion aims to recover a tensor from partially observed noisy entries that may be contaminated with large outliers by exploiting its low-rank property. While there exist several robust tensor completion algorithms, their reliance on singular value decomposition (SVD) limits their scalability. In this paper, we propose a new robust and parallelizable tensor completion method using the tubal rank model. The proposed method rests on tensor factorization, thus averts the costly SVD iterations, and leverages a differentiable, robust correntropy error measure to mitigate the effect of outliers. Leveraging a half-quadratic technique and an alternating steepest descent method, we develop a new SVD-free and parallelizable robust tensor completion algorithm. Numerical results using both synthetic and real data demonstrate the robustness and efficiency of the proposed algorithm.