Regularized Kaczmarz Algorithms for Tensor Recovery

Xuemei Chen, Jing Qin

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

Tensor recovery has recently arisen in a lot of application fields, such as transportation, medical imaging, and remote sensing. Under the assumption that signals possess sparse and/or low-rank structures, many tensor recovery methods have been developed to apply various regularization techniques together with the operator-splitting type of algorithms. Due to the unprecedented growth of data, it becomes increasingly desirable to use streamlined algorithms to achieve real-time compu-tation, such as stochastic optimization algorithms that have recently emerged as an efficient family of methods in machine learning. In this work, we propose a novel algorithmic framework based on the Kaczmarz algorithm for tensor recovery. We provide thorough convergence analysis and its applications from the vector case to the tensor one. Numerical results on a variety of tensor recovery applications, including sparse signal recovery, low-rank tensor recovery, image inpainting, and deconvolution, illustrate the enormous potential of the proposed methods.

Original languageEnglish
Pages (from-to)1439-1471
Number of pages33
JournalSIAM Journal on Imaging Sciences
Volume14
Issue number4
DOIs
StatePublished - 2021

Bibliographical note

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© by SIAM. Unauthorized reproduction of this article is prohibited.

Keywords

  • Kaczmarz algorithm
  • image deblurring
  • image inpainting
  • randomized algorithm
  • tensor recovery

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics

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