Kontak, Max und Michel, Volker (2018) The Regularized Weak Functional Matching Pursuit for linear inverse problems. Journal of Inverse and Ill-posed Problems. de Gruyter. doi: 10.1515/jiip-2018-0013. ISSN 0928-0219. (im Druck)
Es ist eine neuere Version dieses Eintrags verfügbar. |
PDF
889kB |
Offizielle URL: https://www.degruyter.com/view/j/jiip.ahead-of-print/jiip-2018-0013/jiip-2018-0013.xml
Kurzfassung
In this work, we present the so-called Regularized Weak Functional Matching Pursuit (RWFMP) algorithm, which is a weak greedy algorithm for linear ill-posed inverse problems. In comparison to the Regularized Functional Matching Pursuit (RFMP), on which it is based, the RWFMP possesses an improved theoretical analysis including the guaranteed existence of the iterates, the convergence of the algorithm for inverse problems in infinite-dimensional Hilbert spaces, and a convergence rate, which is also valid for the particular case of the RFMP. Another improvement is the cancellation of the previously required and difficult to verify semi-frame condition. Furthermore, we provide an a-priori parameter choice rule for the RWFMP, which yields a convergent regularization. Finally, we will give a numerical example, which shows that the "weak" approach is also beneficial from the computational point of view. By applying an improved search strategy in the algorithm, which is motivated by the weak approach, we can save up to 90% of computation time in comparison to the RFMP, whereas the accuracy of the solution does not change as much.
elib-URL des Eintrags: | https://elib.dlr.de/122987/ | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Dokumentart: | Zeitschriftenbeitrag | ||||||||||||
Zusätzliche Informationen: | The final publication is available at www.degruyter.com. | ||||||||||||
Titel: | The Regularized Weak Functional Matching Pursuit for linear inverse problems | ||||||||||||
Autoren: |
| ||||||||||||
Datum: | 16 Oktober 2018 | ||||||||||||
Erschienen in: | Journal of Inverse and Ill-posed Problems | ||||||||||||
Referierte Publikation: | Ja | ||||||||||||
Open Access: | Ja | ||||||||||||
Gold Open Access: | Nein | ||||||||||||
In SCOPUS: | Ja | ||||||||||||
In ISI Web of Science: | Ja | ||||||||||||
DOI: | 10.1515/jiip-2018-0013 | ||||||||||||
Verlag: | de Gruyter | ||||||||||||
ISSN: | 0928-0219 | ||||||||||||
Status: | im Druck | ||||||||||||
Stichwörter: | Convergence rate, greedy algorithm, ill-posed problem, inverse problem, non-linear approximation, Tikhonov regularization | ||||||||||||
HGF - Forschungsbereich: | Luftfahrt, Raumfahrt und Verkehr | ||||||||||||
HGF - Programm: | Raumfahrt | ||||||||||||
HGF - Programmthema: | Technik für Raumfahrtsysteme | ||||||||||||
DLR - Schwerpunkt: | Raumfahrt | ||||||||||||
DLR - Forschungsgebiet: | R SY - Technik für Raumfahrtsysteme | ||||||||||||
DLR - Teilgebiet (Projekt, Vorhaben): | R - Vorhaben SISTEC (alt) | ||||||||||||
Standort: | Köln-Porz | ||||||||||||
Institute & Einrichtungen: | Institut für Simulations- und Softwaretechnik > High Performance Computing | ||||||||||||
Hinterlegt von: | Kontak, Max | ||||||||||||
Hinterlegt am: | 26 Nov 2018 14:29 | ||||||||||||
Letzte Änderung: | 17 Okt 2019 03:00 |
Verfügbare Versionen dieses Eintrags
- The Regularized Weak Functional Matching Pursuit for linear inverse problems. (deposited 26 Nov 2018 14:29) [Gegenwärtig angezeigt]
Nur für Mitarbeiter des Archivs: Kontrollseite des Eintrags