Inexact Alternating Direction Methods for Image Recovery

Michael K. Ng, Fan Wang, Xiaoming Yuan

Research output: Contribution to journalJournal articlepeer-review

67 Citations (Scopus)
27 Downloads (Pure)


In the image processing community, there have recently been many restoration and reconstruction problems that can be reformulated into linearly constrained convex programming models whose objective functions have separable structures. These favorable reformulations have promoted impressive applications of the alternating direction method (ADM) in the field of image processing. At each iteration, the computation of ADM is dominated by solving two subproblems exactly. However, in many restoration and reconstruction applications, it is either impossible or extremely expensive to obtain exact solutions of these ADM subproblems. This fact urges the development on inexact versions of ADM, which allow the generated ADM subproblems to be solved approximately subject to certain inexactness criteria. In this paper, we develop some truly implementable inexact ADMs whose inexactness criteria controlling the accuracy of the ADM subproblems are easily implementable. The convergence of the new inexact ADMs will be proved. Numerical results on several image processing problems will be given to illustrate the effectiveness of the proposed inexact ADMs.

Original languageEnglish
Pages (from-to)1643-1668
Number of pages26
JournalSIAM Journal on Scientific Computing
Issue number4
Publication statusPublished - 21 Jul 2011

Scopus Subject Areas

  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Alternating direction method
  • Compression
  • Convergence
  • Image reconstruction
  • Image restoration
  • Inexact


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