A multilevel algorithm for simultaneously denoising and deblurring images

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

27 Citations (Scopus)

Abstract

In this paper, we develop a fast multilevel algorithm for simultaneously denoising and deblurring images under the total variation regularization. Although much effort has been devoted to developing fast algorithms for the numerical solut ion and the denoising problem was satisfactorily solved, fast algorithms for the combined denoising and deblurring model remain to be a challenge. Recently several successful studies of approximating this model and subsequently finding fast algorithms were conducted which have partially solved this problem. The aim of this paper is to generalize a fast multilevel denoising method to solving the minimization model for simultaneously denoising and deblurring. Our new idea is to overcome the complexity issue by a detailed study of the structured matrices that are associated with the blurring operator. A fast algorithm can then be obtained for directly solving the variational model. Supporting numerical experiments on gray scale images are presented.

Original languageEnglish
Pages (from-to)1043-1063
Number of pages21
JournalSIAM Journal on Scientific Computing
Volume32
Issue number2
DOIs
Publication statusPublished - Jan 2010
Externally publishedYes

Keywords

  • Denoising and deblurring
  • Image restoration
  • Multilevel methods
  • Total variation
  • Uegularization

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