Bärligea, Adelina und Hochstaffl, Philipp und Schreier, Franz (2023) A Generalized Variable Projection Algorithm for Least Squares Problems in Atmospheric Remote Sensing. Mathematics, 11 (13), Seite 2839. Multidisciplinary Digital Publishing Institute (MDPI). doi: 10.3390/math11132839. ISSN 2227-7390.
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Offizielle URL: https://dx.doi.org/10.3390/math11132839
Kurzfassung
The paper presents a solution for efficiently and accurately solving separable least squares problems with multiple datasets. These problems involve determining linear parameters that are specific to each dataset while ensuring that the nonlinear parameters remain consistent across all datasets. A well-established approach for solving such problems is the variable projection algorithm introduced by Golub and LeVeque, which effectively reduces a separable problem to its nonlinear component. However, this algorithm assumes that the datasets have equal sizes and identical auxiliary model parameters. This article is motivated by a real-world remote sensing application where these assumptions do not apply. Consequently, we propose a generalized algorithm that extends the original theory to overcome these limitations. The new algorithm has been implemented and tested using both synthetic and real satellite data for atmospheric carbon dioxide retrievals. It has also been compared to conventional state-of-the-art solvers, and its advantages are thoroughly discussed. The experimental results demonstrate that the proposed algorithm significantly outperforms all other methods in terms of computation time, while maintaining comparable accuracy and stability. Hence, this novel method can have a positive impact on future applications in remote sensing and could be valuable for other scientific fitting problems with similar properties.
elib-URL des Eintrags: | https://elib.dlr.de/195878/ | ||||||||||||||||
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Dokumentart: | Zeitschriftenbeitrag | ||||||||||||||||
Titel: | A Generalized Variable Projection Algorithm for Least Squares Problems in Atmospheric Remote Sensing | ||||||||||||||||
Autoren: |
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Datum: | 26 Juni 2023 | ||||||||||||||||
Erschienen in: | Mathematics | ||||||||||||||||
Referierte Publikation: | Ja | ||||||||||||||||
Open Access: | Ja | ||||||||||||||||
Gold Open Access: | Ja | ||||||||||||||||
In SCOPUS: | Ja | ||||||||||||||||
In ISI Web of Science: | Ja | ||||||||||||||||
Band: | 11 | ||||||||||||||||
DOI: | 10.3390/math11132839 | ||||||||||||||||
Seitenbereich: | Seite 2839 | ||||||||||||||||
Verlag: | Multidisciplinary Digital Publishing Institute (MDPI) | ||||||||||||||||
ISSN: | 2227-7390 | ||||||||||||||||
Status: | veröffentlicht | ||||||||||||||||
Stichwörter: | separable least squares; nonlinear optimization; python; inverse problems; trace gas retrieval; atmospheric composition; carbon dioxide; infrared spectroscopy | ||||||||||||||||
HGF - Forschungsbereich: | Luftfahrt, Raumfahrt und Verkehr | ||||||||||||||||
HGF - Programm: | Raumfahrt | ||||||||||||||||
HGF - Programmthema: | Erdbeobachtung | ||||||||||||||||
DLR - Schwerpunkt: | Raumfahrt | ||||||||||||||||
DLR - Forschungsgebiet: | R EO - Erdbeobachtung | ||||||||||||||||
DLR - Teilgebiet (Projekt, Vorhaben): | R - Spektroskopische Verfahren der Atmosphäre | ||||||||||||||||
Standort: | Oberpfaffenhofen | ||||||||||||||||
Institute & Einrichtungen: | Institut für Methodik der Fernerkundung > Atmosphärenprozessoren | ||||||||||||||||
Hinterlegt von: | Hochstaffl, Dr. Philipp | ||||||||||||||||
Hinterlegt am: | 07 Jul 2023 10:11 | ||||||||||||||||
Letzte Änderung: | 28 Nov 2023 13:01 |
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