Alternating direction method of multipliers for nonconvex log total variation image restoration

Benxin ZHANG, Guopu ZHU, Zhibin ZHU, Sam KWONG

Research output: Journal PublicationsJournal Article (refereed)peer-review

8 Citations (Scopus)

Abstract

In this paper, we propose a nonconvex log total variation model for image restoration. A specific alternating direction method of multipliers is also presented to solve the nonconvex optimization model. Under mild conditions, we prove that the sequence generated by the proposed alternating direction method of multipliers converges to a stationary point. Experiment results on image denoising, image deblurring, computed tomography, magnetic resonance imaging and image super-resolution demonstrate that the proposed method is effective and improves the quality of image recovery.
Original languageEnglish
Pages (from-to)338-359
Number of pages22
JournalApplied Mathematical Modelling
Volume114
Early online date30 Sept 2022
DOIs
Publication statusPublished - Feb 2023
Externally publishedYes

Bibliographical note

Funding Information:
We are grateful to the editor and anonymous reviewers for their valuable comments which help to improve the presentation of the paper. This work was supported in part by the National Natural Science Foundation of China under Grant 11901137, Grant 62172402, Grant 61872350, and Grant 61967004, in part by the Hong Kong Innovation and Technology Commission (InnoHK Project CIMDA), in part by the Hong Kong RGC GRF under Grant 9042816 (CityU 11209819) and Grant 9042958 (CityU 11203820), and in part by the Fundamental Research Funds for the Central Universities under Grant FRFCU5710011322.

Publisher Copyright:
© 2022 Elsevier Inc.

Keywords

  • Alternating direction method of multipliers
  • Convergence
  • Image restoration
  • Log total variation
  • Nonconvex optimization

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