Efficient Tensor Completion for Color Image and Video Recovery: Low-Rank Tensor Train

Johann A. Bengua, Ho N. Phien, Hoang Duong Tuan, Minh N. Do

Research output: Contribution to journalArticlepeer-review


This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks to its definition from a well-balanced matricization scheme. Accordingly, new optimization formulations for tensor completion are proposed as well as two new algorithms for their solution. The first one called simple low-rank tensor completion via TT (SiLRTC-TT) is intimately related to minimizing a nuclear norm based on TT rank. The second one is from a multilinear matrix factorization model to approximate the TT rank of a tensor, and is called tensor completion by parallel matrix factorization via TT (TMac-TT). A tensor augmentation scheme of transforming a low-order tensor to higher orders is also proposed to enhance the effectiveness of SiLRTC-TT and TMac-TT. Simulation results for color image and video recovery show the clear advantage of our method over all other methods.

Original languageEnglish (US)
Article number7859390
Pages (from-to)2466-2479
Number of pages14
JournalIEEE Transactions on Image Processing
Issue number5
StatePublished - May 2017


  • Color image recovery
  • Tucker decomposition
  • tensor completion
  • tensor train decomposition
  • tensor train nuclear norm
  • tensor train rank
  • video recovery

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design


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