title: The specifics of method of consecutive projections in deconvolution problems
metadata.name: dc.contributor.author
metadata.value: Latypov, Iskander Sh.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2019-05-24T08:25:55Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2019-05-24T08:25:55Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2019-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Latypov I. Sh. The specifics of method of consecutive projections in deconvolution problems. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2019, vol. 6 (64), issue 1, pp. 81–87.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2019.105
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/15538
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Method of consecutive projections (MCP) is quite popular. The principal idea of the method is to present the convex set as intersection of simple elementary convex sets and project to sets, outer for the current point. To build projection onto elementary sets very easy, because elementary sets are semispaces. It was proved, that this algorithm is ﬁnitely convergent. Each iteration of MCP has 3 tasks: 1. choose elementary set for projection; 2. deﬁne direction; 3. calculate length of step. Typical features of the method for deconvolution problems are the large dimension and the presence of a large number of almost perpendicular directions of projection. We found that several sequential steps in perpendicular directions can be replaced by one step, indicating a simple way to build it. Although the theoretical speed of convergence of the method remained the same, for large-scale problems (of the order of hundreds of millions), characteristic, for example, for image processing, it was possible to reduce the counting time by hundreds of times.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 6 (64); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: convex programming
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: projection onto set
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: method of consecutive projections
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: deconvolution
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: The specifics of method of consecutive projections in deconvolution problems
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 81-87.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/15538/1/81-87.pdf
resources.format: Adobe PDF
resources.size: 268,23 kB