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A Generalized Variable Projection Algorithm for Least Squares Problems in Atmospheric Remote Sensing

Bärligea, Adelina and Hochstaffl, Philipp and Schreier, Franz (2023) A Generalized Variable Projection Algorithm for Least Squares Problems in Atmospheric Remote Sensing. Mathematics, 11 (13), p. 2839. Multidisciplinary Digital Publishing Institute (MDPI). doi: 10.3390/math11132839. ISSN 2227-7390.

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Official URL: https://dx.doi.org/10.3390/math11132839


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.

Item URL in elib:https://elib.dlr.de/195878/
Document Type:Article
Title:A Generalized Variable Projection Algorithm for Least Squares Problems in Atmospheric Remote Sensing
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Bärligea, AdelinaDLR IMFhttps://orcid.org/0009-0008-5497-1941UNSPECIFIED
Hochstaffl, PhilippUNSPECIFIEDhttps://orcid.org/0000-0001-9537-3050UNSPECIFIED
Schreier, FranzUNSPECIFIEDhttps://orcid.org/0000-0001-7196-6599UNSPECIFIED
Date:26 June 2023
Journal or Publication Title:Mathematics
Refereed publication:Yes
Open Access:Yes
Gold Open Access:Yes
In ISI Web of Science:Yes
Page Range:p. 2839
Publisher:Multidisciplinary Digital Publishing Institute (MDPI)
Keywords:separable least squares; nonlinear optimization; python; inverse problems; trace gas retrieval; atmospheric composition; carbon dioxide; infrared spectroscopy
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Earth Observation
DLR - Research area:Raumfahrt
DLR - Program:R EO - Earth Observation
DLR - Research theme (Project):R - Spectroscopic methods of the atmosphere
Location: Oberpfaffenhofen
Institutes and Institutions:Remote Sensing Technology Institute > Atmospheric Processors
Deposited By: Hochstaffl, Dr. Philipp
Deposited On:07 Jul 2023 10:11
Last Modified:28 Nov 2023 13:01

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