The implicit convex feasibility problem and its application to adaptive image denoising

Yair Censor, Aviv Gibali, Frank Lenzen, Christoph Schnörr

Research output: Contribution to journalArticlepeer-review


The implicit convex feasibility problem attempts to find a point in the intersection of a finite family of convex sets, some of which are not explicitly determined but may vary. We develop simultaneous and sequential projection methods capable of handling such problems and demonstrate their applicability to image denoising in a specific medical imaging situation. By allowing the variable sets to undergo scaling, shifting and rotation, this work generalizes previous results wherein the implicit convex feasibility problem was used for cooperative wireless sensor network positioning where sets are balls and their centers were implicit.

Original languageEnglish
Pages (from-to)610-625
Number of pages16
JournalJournal of Computational Mathematics
Issue number6
StatePublished - 1 Nov 2016

Bibliographical note

Funding Information:
We thank the anonymous referees for their comments and suggestions which helped us improve the paper. The first author's work was supported by Research Grant No. 2013003 of the United States-Israel Binational Science Foundation (BSF).

Publisher Copyright:
Copyright 2016 by AMSS, Chinese Academy of Science.


  • Image denoising
  • Implicit convex feasibility
  • Projection methods
  • Proximity function
  • Split feasibility
  • Variable sets

ASJC Scopus subject areas

  • Computational Mathematics


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