Projection methods for finding intersection of two convex sets and their use in signal processing problems

0545397 - ÚTIA 2022 RIV US eng C - Conference Paper (international conference)
Bílková, Zuzana - Šorel, Michal
Projection methods for finding intersection of two convex sets and their use in signal processing problems.
Image Processing: Algorithms and Systems XIX. Springfield: Society for Imaging Science and Technology, 2021, č. článku 226. E-ISSN 2470-1173.
[Image Processing: Algorithms and Systems 2021 /19./. Springfield (Online) (US), 11.01.2021-28.01.2021]
R&D Projects: GA ČR GA18-05360S
Grant - others:GA UK(CZ) 1583117; GA MŠk(CZ) SVV-2017-260452
Institutional support: RVO:67985556
Keywords : POCS * Dykstra's projection algorithm * ADMM * JPEG
OECD category: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
http://library.utia.cas.cz/separaty/2021/ZOI/bilkova-0545397.pdf

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.

Permanent Link: http://hdl.handle.net/11104/0322144