Continuation method for total variation denoising problems

Tony F. CHAN, H. M. ZHOU, Raymond H. CHAN

Research output: Book Chapters | Papers in Conference ProceedingsConference paper (refereed)Researchpeer-review

41 Citations (Scopus)

Abstract

The denoising problem can be solved by posing it as a constrained minimization problem. The objective function is the TV norm of the denoised image whereas the constraint is the requirement that the denoised image does not deviate too much from the observed image. The Euler-Lagrangian equation corresponding to the minimization problem is a nonlinear equation. The Newton method for such equation is known to have a very small domain of convergence. In this paper, we propose to couple the Newton method with the continuation method. Using the Newton-Kantorovich theorem, we give a bound on the domain of convergence. Numerical results are given to illustrate the convergence.

Original languageEnglish
Title of host publicationProceedings of SPIE : Advanced Signal Processing Algorithms
EditorsFranklin T. LUK
PublisherSPIE
Pages314-325
Number of pages12
ISBN (Print)9780819419224
DOIs
Publication statusPublished - 7 Jun 1995
Externally publishedYes
EventSPIE 1995 International Symposium on Optical Science, Engineering, and Instrumentation - San Diego, United States
Duration: 9 Jul 199514 Jul 1995

Publication series

NameProceedings of SPIE : The International Society for Optical Engineering
PublisherSPIE
Volume2563
ISSN (Print)0277-786X

Conference

ConferenceSPIE 1995 International Symposium on Optical Science, Engineering, and Instrumentation
Country/TerritoryUnited States
CitySan Diego
Period9/07/9514/07/95

Bibliographical note

Acknowledgment: The first author would like to acknowledge the hospitality of the Department of Mathematics at the Chinese University of Hong Kong where this work was initiated during a visit.
Publisher Copyright: © 2015 SPIE. All Rights Reserved.

Keywords

  • Denoising
  • Fixed-point method
  • Newton method
  • Total-variation

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