Orthogonal tubal rank-1 tensor pursuit for tensor completion

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

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Author(s)

  • Weize Sun
  • Lei Huang
  • H.C. So
  • Jiajia Wang

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)213-224
Journal / PublicationSignal Processing
Volume157
Online published27 Nov 2018
Publication statusPublished - Apr 2019

Abstract

This work addresses the issue of tensor completion. The properties of the tensor tubal rank are firstly discussed. It is shown that the tensor tubal rank has similar properties like that of matrix rank derived from SVD. The completion algorithm for the case that the measurements are noise-free or corrupted by Gaussian noise is then proposed based on an orthogonal pursuit on tubal rank-1 tensors. The philosophy behind the devised approach is to relax the problem of tensor tubal rank minimization into tensor Frobenius-norm optimization with a constraint on the maximum number of orthogonal tensors. An iterative procedure which calculates one orthogonal tensor at each iterative step is then suggested, and the local convergence under the noise-free case is also proved. Furthermore, the proposed method is generalized to the situation where the observations are corrupted by impulsive noise in a tubal form. To tackle the impulsive noise, we formulate the problem of tensor completion as minimization of tensor tubal ℓp-norm with 1 < p < 2. An iteratively reweighted procedure is employed to compute the orthogonal tensors. The algorithms are compared with the state-of-the-art approaches using both synthetic data and real data sets.

Research Area(s)

  • Rank-one tensor, Tensor completion, Tensor pursuit, Tensor SVD, Tensor tubal rank

Citation Format(s)

Orthogonal tubal rank-1 tensor pursuit for tensor completion. / Sun, Weize; Huang, Lei; So, H.C.; Wang, Jiajia.

In: Signal Processing, Vol. 157, 04.2019, p. 213-224.

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