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Volume 34, Issue 6
The Implicit Convex Feasibility Problem and Its Application to Adaptive Image Denoising

Yair Censor, Aviv Gibali, Frank Lenzen & Christoph Schnörr

DOI: 10.4208/jcm.1606-m2016-0581

J. Comp. Math., 34 (2016), pp. 610-625.

Published online: 2016-12

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  • Abstract

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.

  • Keywords

Implicit convex feasibility, Split feasibility, projection methods, Variable sets, Proximity function, Image denoising.

  • AMS Subject Headings

52A20, 65K15, 90C25, 90C90.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

yair@math.haifa.ac.il (Yair Censor)

avivg@braude.ac.il (Aviv Gibali)

frank.lenzen@iwr.uni-heidelberg.de (Frank Lenzen)

schnoerr@math.uni-heidelberg.de (Christoph Schnörr)

  • BibTex
  • RIS
  • TXT
@Article{JCM-34-610, author = {Censor , YairGibali , AvivLenzen , Frank and Schnörr , Christoph}, title = {The Implicit Convex Feasibility Problem and Its Application to Adaptive Image Denoising}, journal = {Journal of Computational Mathematics}, year = {2016}, volume = {34}, number = {6}, pages = {610--625}, abstract = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1606-m2016-0581}, url = {http://global-sci.org/intro/article_detail/jcm/9816.html} }
TY - JOUR T1 - The Implicit Convex Feasibility Problem and Its Application to Adaptive Image Denoising AU - Censor , Yair AU - Gibali , Aviv AU - Lenzen , Frank AU - Schnörr , Christoph JO - Journal of Computational Mathematics VL - 6 SP - 610 EP - 625 PY - 2016 DA - 2016/12 SN - 34 DO - http://doi.org/10.4208/jcm.1606-m2016-0581 UR - https://global-sci.org/intro/article_detail/jcm/9816.html KW - Implicit convex feasibility, Split feasibility, projection methods, Variable sets, Proximity function, Image denoising. AB -

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.

Censor , YairGibali , AvivLenzen , Frank and Schnörr , Christoph. (2016). The Implicit Convex Feasibility Problem and Its Application to Adaptive Image Denoising. Journal of Computational Mathematics. 34 (6). 610-625. doi:10.4208/jcm.1606-m2016-0581
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