Luke, Russell

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[["dc.bibliographiccitation.firstpage","63"],["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","Journal of Approximation Theory"],["dc.bibliographiccitation.lastpage","69"],["dc.bibliographiccitation.volume","141"],["dc.contributor.author","Bauschke, Heinz H."],["dc.contributor.author","Combettes, Patrick L."],["dc.contributor.author","Luke, Russell"],["dc.date.accessioned","2017-09-07T11:50:10Z"],["dc.date.available","2017-09-07T11:50:10Z"],["dc.date.issued","2006"],["dc.description.abstract","A new iterative method for finding the projection onto the intersection of two closed convex sets in a Hilbert space is presented. It is a Haugazeau-like modification of a recently proposed averaged alternating reflections method which produces a strongly convergent sequence."],["dc.identifier.doi","10.1016/j.jat.2006.01.003"],["dc.identifier.gro","3147601"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/5081"],["dc.language.iso","en"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","0021-9045"],["dc.title","A strongly convergent reflection method for finding the projection onto the intersection of two closed convex sets in a Hilbert space"],["dc.type","journal_article"],["dc.type.internalPublication","no"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","841"],["dc.bibliographiccitation.lastpage","844"],["dc.bibliographiccitation.volume","3"],["dc.contributor.author","Bauschke, Heinz H."],["dc.contributor.author","Combettes, Patrick L."],["dc.contributor.author","Luke, Russell"],["dc.date.accessioned","2017-09-07T11:50:31Z"],["dc.date.available","2017-09-07T11:50:31Z"],["dc.date.issued","2002"],["dc.description.abstract","The state of the art for solving the phase retrieval problem in two dimensions relies heavily on the algorithms proposed by Gerchbercy, Saxton, and Fienup. Despite the widespread use of these algorithms, current mathematical theory cannot explain their remarkable success. It is already known that the Gerchberg-Saxton algorithm is a nonconvex version of method of alternating projections. In this paper, we show that two other prominent phase retrieval methods also have well known counterparts in the world of convex optimization algorithms: Fienup's basic input-output algorithm corresponds to Dykstra's algorithm, and Fienup's hybrid input-output algorithm can be viewed as an instance of the Douglas-Rachford algorithm. This work provides a theoretical framework to better understand and, potentially, improve existing phase recovery algorithms."],["dc.identifier.doi","10.1109/icip.2002.1040082"],["dc.identifier.gro","3147615"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/5087"],["dc.language.iso","en"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.publisher","IEEE"],["dc.relation.conference","International Conference on Image Processing"],["dc.relation.eventend","2002-09-25"],["dc.relation.eventlocation","Rochester, New York, USA"],["dc.relation.eventstart","2002-09-22"],["dc.relation.isbn","0-7803-7622-6"],["dc.relation.ispartof","Proceedings. 2002 International Conference on Image Processing"],["dc.title","On the structure of some phase retrieval algorithms"],["dc.type","conference_paper"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

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[["dc.bibliographiccitation.firstpage","63"],["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","Foundations of Computational Mathematics"],["dc.bibliographiccitation.lastpage","83"],["dc.bibliographiccitation.volume","14"],["dc.contributor.author","Bauschke, Heinz H."],["dc.contributor.author","Luke, Russell"],["dc.contributor.author","Phan, Hung M."],["dc.contributor.author","Wang, Xianfu"],["dc.date.accessioned","2017-09-07T11:50:05Z"],["dc.date.available","2017-09-07T11:50:05Z"],["dc.date.issued","2013"],["dc.identifier.doi","10.1007/s10208-013-9161-0"],["dc.identifier.gro","3147587"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/5071"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.publisher","Springer Nature"],["dc.relation.issn","1615-3375"],["dc.title","Restricted Normal Cones and Sparsity Optimization with Affine Constraints"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

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