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Iterative algorithms for a non-linear inverse problem in atmospheric lidar

Denevi, G; Garbarino, S; Sorrentino, A; (2017) Iterative algorithms for a non-linear inverse problem in atmospheric lidar. Inverse Problems , 33 , Article 085010. 10.1088/1361-6420/aa7904. Green open access

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Abstract

We consider the inverse problem of retrieving aerosol extinction coefficients from Raman lidar measurements. In this problem the unknown and the data are related through the exponential of a linear operator, the unknown is non– negative and the data follow the Poisson distribution. Standard methods work on the log–transformed data and solve the resulting linear inverse problem, but neglect to take into account the noise statistics. In this study we show that proper modelling of the noise distribution can improve substantially the quality of the reconstructed extinction profiles. To achieve this goal, we consider the non–linear inverse problem with non– negativity constraint, and propose two iterative algorithms derived using the KarushKuhn-Tucker conditions. We validate the algorithms with synthetic and experimental data. As expected, the proposed algorithms out–perform standard methods in terms of sensitivity to noise and reliability of the estimated profile.

Type: Article
Title: Iterative algorithms for a non-linear inverse problem in atmospheric lidar
Open access status: An open access version is available from UCL Discovery
DOI: 10.1088/1361-6420/aa7904
Publisher version: http://doi.org/10.1088/1361-6420/aa7904
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: http://discovery.ucl.ac.uk/id/eprint/1571684
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