Parameterizations for ensemble Kalman inversion

Chada, Neil and Iglesias, Marco and Lassi, Roininen and Stuart, Andrew M. (2018) Parameterizations for ensemble Kalman inversion. Inverse Problems, 34 (5). 055009. ISSN 0266-5611

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Abstract

The use of ensemble methods to solve inverse problems is attractive because it is a derivative-free methodology which is also well-adapted to parallelization. In its basic iterative form the method produces an ensemble of solutions which lie in the linear span of the initial ensemble. Choice of the parameterization of the unknown field is thus a key component of the success of the method. We demonstrate how both geometric ideas and hierarchical ideas can be used to design effective parameterizations for a number of applied inverse problems arising in electrical impedance tomography, groundwater flow and source inversion. In particular we show how geometric ideas, including the level set method, can be used to reconstruct piecewise continuous fields, and we show how hierarchical methods can be used to learn key parameters in continuous fields, such as length-scales, resulting in improved reconstructions. Geometric and hierarchical ideas are combined in the level set method to find piecewise constant reconstructions with interfaces of unknown topology.

Item Type: Article
RIS ID: https://nottingham-repository.worktribe.com/output/934544
Additional Information: This is an author-created, un-copyedited version of an article accepted for publication/published in Inverse Problems. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1361-6420/aab6d9.
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1088/1361-6420/aab6d9
Depositing User: Iglesias Hernandez, Marco
Date Deposited: 04 May 2018 08:55
Last Modified: 04 May 2020 19:37
URI: http://eprints.nottingham.ac.uk/id/eprint/51560

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