On the convergence of nonconvex minimization methods for image recovery

Jin Xiao, Kwok Po NG, Yu Fei Yang

Research output: Contribution to journalJournal articlepeer-review

19 Citations (Scopus)


Nonconvex nonsmooth regularization method has been shown to be effective for restoring images with neat edges. Fast alternating minimization schemes have also been proposed and developed to solve the nonconvex nonsmooth minimization problem. The main contribution of this paper is to show the convergence of these alternating minimization schemes, based on the Kurdyka-Łojasiewicz property. In particular, we show that the iterates generated by the alternating minimization scheme, converges to a critical point of this nonconvex nonsmooth objective function. We also extend the analysis to nonconvex nonsmooth regularization model with box constraints, and obtain similar convergence results of the related minimization algorithm. Numerical examples are given to illustrate our convergence analysis.

Original languageEnglish
Article number7035035
Pages (from-to)1587-1598
Number of pages12
JournalIEEE Transactions on Image Processing
Issue number5
Publication statusPublished - 1 May 2015

Scopus Subject Areas

  • Software
  • Computer Graphics and Computer-Aided Design

User-Defined Keywords

  • alternating minimization methods
  • box-constraints
  • Image restoration
  • Kurdykalojasiewicz inequality
  • nonconvex and nonsmooth


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