About: Hilbert-space techniques for spectral representation in terms of overcomplete bases

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Topics associated with the representation of objects from a separable Hilbert space in terms of an a priori given overcomplete system (dictionary) of its generators (atoms) are handled. First the procedure of finding such a representation is formulated and solved using the Hilbert-space technique of linear bounded operators and their generalized inverse. Afterwards the problem of finding its sparse representation is discussed, i.e. such representation where most information on the given object is concentrated in a fewest possible number of its nonzero (spectral) coefficients in that representation. This may be rephrased as a procedure for finding a subbasis which is in a certain sense optimal for the given object in the scope of the prescribed overcomplete system. In general the common approach based on Moore-Penrose pseudoinverse does not yield the desired sparse solutions. That is why alternate procedures are discussed, in particular from the point of view of their numerical stability and computatio Topics associated with the representation of objects from a separable Hilbert space in terms of an a priori given overcomplete system (dictionary) of its generators (atoms) are handled. First the procedure of finding such a representation is formulated and solved using the Hilbert-space technique of linear bounded operators and their generalized inverse. Afterwards the problem of finding its sparse representation is discussed, i.e. such representation where most information on the given object is concentrated in a fewest possible number of its nonzero (spectral) coefficients in that representation. This may be rephrased as a procedure for finding a subbasis which is in a certain sense optimal for the given object in the scope of the prescribed overcomplete system. In general the common approach based on Moore-Penrose pseudoinverse does not yield the desired sparse solutions. That is why alternate procedures are discussed, in particular from the point of view of their numerical stability and computatio (en) Topics associated with the representation of objects from a separable Hilbert space in terms of an a priori given overcomplete system (dictionary) of its generators (atoms) are handled. First the procedure of finding such a representation is formulated and solved using the Hilbert-space technique of linear bounded operators and their generalized inverse. Afterwards the problem of finding its sparse representation is discussed, i.e. such representation where most information on the given object is concentrated in a fewest possible number of its nonzero (spectral) coefficients in that representation. This may be rephrased as a procedure for finding a subbasis which is in a certain sense optimal for the given object in the scope of the prescribed overcomplete system. In general the common approach based on Moore-Penrose pseudoinverse does not yield the desired sparse solutions. That is why alternate procedures are discussed, in particular from the point of view of their numerical stability and computatio (cs)
Title	Hilbert-space techniques for spectral representation in terms of overcomplete bases Hilbert-space techniques for spectral representation in terms of overcomplete bases (en) Hilbert-space techniques for spectral representation in terms of overcomplete bases (cs)
skos:prefLabel	Hilbert-space techniques for spectral representation in terms of overcomplete bases Hilbert-space techniques for spectral representation in terms of overcomplete bases (en) Hilbert-space techniques for spectral representation in terms of overcomplete bases (cs)
skos:notation	RIV/00216224:14310/02:00007145!RIV08-MSM-14310___
http://linked.open.../vavai/riv/strany	259
http://linked.open...avai/riv/aktivita	Z
http://linked.open...avai/riv/aktivity	Z(MSM 143100001)
http://linked.open...vai/riv/dodaniDat	2008
http://linked.open...aciTvurceVysledku	Veselý, Vítězslav
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Masarykova univerzita / Přírodovědecká fakulta
http://linked.open...dnocenehoVysledku	647621
http://linked.open...ai/riv/idVysledku	RIV/00216224:14310/02:00007145
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	functional approximation; kernel operators; frame and wavelet expansions; pseudoinverse operators (en)
http://linked.open.../riv/klicoveSlovo	frame and wavelet expansions kernel operators pseudoinverse operators functional approximation
http://linked.open...ontrolniKodProRIV	[1C0249C80BD9]
http://linked.open...v/mistoKonaniAkce	August 2001, Čihák near Žamberk (Northeast Bohem
http://linked.open...i/riv/mistoVydani	Brno (Czech Rep.)
http://linked.open...i/riv/nazevZdroje	Proceedings of the Summer School DATASTAT'2001, Folia Fac. Sci. Nat. Univ. Masaryk. Brunensis, Mathematica 11
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...UplatneniVysledku	2002
http://linked.open...iv/tvurceVysledku	Veselý, Vítězslav
http://linked.open...vavai/riv/typAkce	CST - Celostátní
http://linked.open.../riv/zahajeniAkce	2001-01-01 (xsd:date)
http://linked.open...n/vavai/riv/zamer	http://linked.opendata.cz/resource/domain/vavai/zamer/MSM%20143100001
number of pages	15 (xsd:int)
http://purl.org/ne...btex#hasPublisher	Masaryk University
https://schema.org/isbn	80-210-3028-3
http://localhost/t...ganizacniJednotka	14310

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