Nonstationary iterated thresholding algorithms for image deblurring

Jie HUANG, Marco DONATELLI, Raymond CHAN

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

25 Citations (Scopus)

Abstract

We propose iterative thresholding algorithms based on the iterated Tikhonov method for image deblurring problems. Our method is similar in idea to the modified linearized Bregman algorithm (MLBA) so is easy to implement. In order to obtain good restorations, MLBA requires an accurate estimate of the regularization parameter α which is hard to get in real applications. Based on previous results in iterated Tikhonov method, we design two nonstationary iterative thresholding algorithms which give near optimal results without estimating α. One of them is based on the iterative soft thresholding algorithm and the other is based on MLBA. We show that the nonstationary methods, if converge, will converge to the same minimizers of the stationary variants. Numerical results show that the accuracy and convergence of our nonstationary methods are very robust with respect to the changes in the parameters and the restoration results are comparable to those of MLBA with optimal α.

Original languageEnglish
Pages (from-to)717-736
Number of pages20
JournalInverse Problems and Imaging
Volume7
Issue number3
DOIs
Publication statusPublished - Aug 2013
Externally publishedYes

Keywords

  • Image deblurring
  • Iterated Tikhonov
  • Linearized Bregman iteration
  • Nonstationary parameter sequence
  • Soft thresholding

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