Publikation: Algebraic compressed sensing
Dateien
Datum
Autor:innen
Herausgeber:innen
ISSN der Zeitschrift
Electronic ISSN
ISBN
Bibliografische Daten
Verlag
Schriftenreihe
Auflagebezeichnung
DOI (zitierfähiger Link)
Internationale Patentnummer
Angaben zur Forschungsförderung
Projekt
Open Access-Veröffentlichung
Sammlungen
Core Facility der Universität Konstanz
Titel in einer weiteren Sprache
Publikationstyp
Publikationsstatus
Erschienen in
Zusammenfassung
We introduce the broad subclass of algebraic compressed sensing problems, where structured signals are modeled either explicitly or implicitly via polynomials. This includes, for instance, low-rank matrix and tensor recovery. We employ powerful techniques from algebraic geometry to study well-posedness of sufficiently general compressed sensing problems, including existence, local recoverability, global uniqueness, and local smoothness. Our main results are summarized in thirteen questions and answers in algebraic compressed sensing. Most of our answers concerning the minimum number of required measurements for existence, recoverability, and uniqueness of algebraic compressed sensing problems are optimal and depend only on the dimension of the model.
Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
Schlagwörter
Konferenz
Rezension
Zitieren
ISO 690
BREIDING, Paul, Fulvio GESMUNDO, Mateusz MICHALEK, Nick VANNIEUWENHOVEN, 2023. Algebraic compressed sensing. In: Applied and Computational Harmonic Analysis. Elsevier. 2023, 65, pp. 374-406. ISSN 1063-5203. eISSN 1096-603X. Available under: doi: 10.1016/j.acha.2023.03.006BibTex
@article{Breiding2023Algeb-66966, year={2023}, doi={10.1016/j.acha.2023.03.006}, title={Algebraic compressed sensing}, volume={65}, issn={1063-5203}, journal={Applied and Computational Harmonic Analysis}, pages={374--406}, author={Breiding, Paul and Gesmundo, Fulvio and Michalek, Mateusz and Vannieuwenhoven, Nick} }
RDF
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#" xmlns:foaf="http://xmlns.com/foaf/0.1/" xmlns:void="http://rdfs.org/ns/void#" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > <rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/66966"> <dc:creator>Michalek, Mateusz</dc:creator> <dc:creator>Vannieuwenhoven, Nick</dc:creator> <dcterms:issued>2023</dcterms:issued> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2023-05-25T13:48:49Z</dcterms:available> <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/66966"/> <dc:contributor>Gesmundo, Fulvio</dc:contributor> <dcterms:abstract>We introduce the broad subclass of algebraic compressed sensing problems, where structured signals are modeled either explicitly or implicitly via polynomials. This includes, for instance, low-rank matrix and tensor recovery. We employ powerful techniques from algebraic geometry to study well-posedness of sufficiently general compressed sensing problems, including existence, local recoverability, global uniqueness, and local smoothness. Our main results are summarized in thirteen questions and answers in algebraic compressed sensing. Most of our answers concerning the minimum number of required measurements for existence, recoverability, and uniqueness of algebraic compressed sensing problems are optimal and depend only on the dimension of the model.</dcterms:abstract> <dc:contributor>Michalek, Mateusz</dc:contributor> <foaf:homepage rdf:resource="http://localhost:8080/"/> <dc:creator>Breiding, Paul</dc:creator> <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dc:creator>Gesmundo, Fulvio</dc:creator> <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/> <dc:contributor>Breiding, Paul</dc:contributor> <dc:contributor>Vannieuwenhoven, Nick</dc:contributor> <dc:language>eng</dc:language> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2023-05-25T13:48:49Z</dc:date> <dcterms:title>Algebraic compressed sensing</dcterms:title> </rdf:Description> </rdf:RDF>