Tensor Factorization with Total Variation and Tikhonov Regularization for Low-Rank Tensor Completion in Imaging Data

Xue-Lei Lin, Michael K. Ng, Xi-Le Zhao*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

11 Citations (Scopus)

Abstract

The main aim of this paper is to study tensor factorization for low-rank tensor completion in imaging data. Due to the underlying redundancy of real-world imaging data, the low-tubal-rank tensor factorization (the tensor–tensor product of two factor tensors) can be used to approximate such tensor very well. Motivated by the spatial/temporal smoothness of factor tensors in real-world imaging data, we propose to incorporate a hybrid regularization combining total variation and Tikhonov regularization into low-tubal-rank tensor factorization model for low-rank tensor completion problem. We also develop an efficient proximal alternating minimization (PAM) algorithm to tackle the corresponding minimization problem and establish a global convergence of the PAM algorithm. Numerical results on color images, color videos, and multispectral images are reported to illustrate the superiority of the proposed method over competing methods.

Original languageEnglish
Pages (from-to)900-918
Number of pages19
JournalJournal of Mathematical Imaging and Vision
Volume62
Issue number6-7
Early online date5 Dec 2019
DOIs
Publication statusPublished - 1 Jul 2020

Scopus Subject Areas

  • Statistics and Probability
  • Modelling and Simulation
  • Condensed Matter Physics
  • Computer Vision and Pattern Recognition
  • Geometry and Topology
  • Applied Mathematics

User-Defined Keywords

  • Hybrid regularization
  • Proximal alternating minimization
  • Tensor completion
  • Tensor factorization

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