Low tubal rank tensor completion using alternating minimization
The low tubal rank tensors have been recently proposed to model real world multidimensional data. In this paper, we study the low tubal rank tensor completion problem, i.e. to recover a third order tensor by observing a subset of elements selected uniform at random. We propose a fast iterative algorithm, called Tubal Alt Min, that is inspired by similar approach for low rank matrix completion. The unknown low tubal rank tensor is parameterized as the product of two much smaller tensors with the low tubal rank property being automatically incorporated, and Tubal Alt Min alternates between estimating those two tensors using tensor least squares minimization. We note that the tensor least squares minimization is different from its counterpart and nontrivial, and this paper gives a routine to carry out this operation. Further, on both synthetic data and real world video data, evaluation results show that compared with the tensor nuclear norm minimization, the proposed algorithm improves the recovery error by orders of magnitude with smaller running time for higher sampling rates.
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