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Volume: 33 | Article ID: art00002
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Projection methods for finding intersection of two convex sets and their use in signal processing problems
  DOI :  10.2352/ISSN.2470-1173.2021.10.IPAS-226  Published OnlineJanuary 2021
Abstract

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.

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Zuzana Bílková, Michal Šorel, "Projection methods for finding intersection of two convex sets and their use in signal processing problemsin Proc. IS&T Int’l. Symp. on Electronic Imaging: Image Processing: Algorithms and Systems XIX,  2021,  pp 226-1 - 226-6,  https://doi.org/10.2352/ISSN.2470-1173.2021.10.IPAS-226

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