Sparse and Truncated Nuclear Norm Based Tensor Completion

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)729-743
Number of pages14
Journal / PublicationNeural Processing Letters
Issue number3
Publication statusPublished - Jun 2017


One of the main difficulties in tensor completion is the calculation of the tensor rank. Recently a tensor nuclear norm, which is equal to the weighted sum of matrix nuclear norms of all unfoldings of the tensor, was proposed to address this issue. However, in this approach, all the singular values are minimized simultaneously. Hence the tensor rank may not be well approximated. In addition, many existing algorithms ignore the structural information of the tensor. This paper presents a tensor completion algorithm based on the proposed tensor truncated nuclear norm, which is superior to the traditional tensor nuclear norm. Furthermore, to maintain the structural information, a sparse regularization term, defined in the transform domain, is added into the objective function. Experimental results showed that our proposed algorithm outperforms several state-of-the-art tensor completion schemes.

Research Area(s)

  • Multi-dimensional DCT, Tensor completion, Truncated nuclear norm

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