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Projection methods for finding intersection of two convex sets and their use in signal processing problems
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SYSNO ASEP 0545397 Document Type C - Proceedings Paper (int. conf.) R&D Document Type Conference Paper Title Projection methods for finding intersection of two convex sets and their use in signal processing problems Author(s) Bílková, Zuzana (UTIA-B) ORCID
Šorel, Michal (UTIA-B) RID, ORCIDNumber of authors 2 Article number 226 Source Title Image Processing: Algorithms and Systems XIX. - Springfield : Society for Imaging Science and Technology, 2021 Number of pages 6 s. Publication form Online - E Action Image Processing: Algorithms and Systems 2021 /19./ Event date 11.01.2021 - 28.01.2021 VEvent location Springfield (Online) Country US - United States Event type WRD Language eng - English Country US - United States Keywords POCS ; Dykstra's projection algorithm ; ADMM ; JPEG Subject RIV IN - Informatics, Computer Science OECD category Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) R&D Projects GA18-05360S GA ČR - Czech Science Foundation (CSF) Institutional support UTIA-B - RVO:67985556 DOI 10.2352/ISSN.2470-1173.2021.10.IPAS-226 Annotation Finding a point in the intersection of two closed convex sets is a common problem in image processing and other areas. Projections onto convex sets (POCS) is a standard algorithm for finding such a point. Dykstra’s projection algorithm is a well known alternative that finds the point in the intersection closest to a given point. Yet another lesser known alternative is the alternating direction method of multipliers (ADMM) that can be used for both purposes. In this paper we discuss the differences in the convergence of these algorithms in image processing problems. The ADMM applied to finding an arbitrary point in the intersection is much faster than POCS and any algorithm for finding the nearest point in the intersection.
Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2022
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