Continuation method for total variation denoising problems

Tony F. Chan, H. M. Zhou, Raymond H. Chan

Research output: Contribution to journalConference articlepeer-review

41 Scopus citations

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 (US)
Pages (from-to)314-325
Number of pages12
JournalProceedings of SPIE - The International Society for Optical Engineering
Volume2563
DOIs
StatePublished - 1995
Externally publishedYes
EventAdvanced Signal Processing Algorithms - San Diego, United States
Duration: Jul 9 1995 → …

Bibliographical note

Publisher Copyright:
© 2015 SPIE. All Rights Reserved.

Keywords

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

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering

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