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The goal of tensor completion is to recover a tensor from a subset of itsentries, often by exploiting its low-rank property. Among several usefuldefinitions of tensor rank, the low-tubal-rank was shown to give a valuablecharacterization of the inherent low-rank structure of a tensor. While somelow-tubal-rank tensor completion algorithms with favorable performance havebeen recently proposed, these algorithms utilize second-order statistics tomeasure the error residual, which may not work well when the observed entriescontain large outliers. In this paper, we propose a new objective function forlow-tubal-rank tensor completion, which uses correntropy as the error measureto mitigate the effect of the outliers. To efficiently optimize the proposedobjective, we leverage a half-quadratic minimization technique whereby theoptimization is transformed to a weighted low-tubal-rank tensor factorizationproblem. Subsequently, we propose two simple and efficient algorithms to obtainthe solution and provide their convergence and complexity analysis. Numericalresults using both synthetic and real data demonstrate the robust and superiorperformance of the proposed algorithms.

Robust Low-tubal-rank Tensor Completion based on Tensor Factorization and Maximum Correntopy Criterion