University of Oulu

Neil K Chada et al 2018 Inverse Problems 34 055009.

Parameterizations for ensemble Kalman inversion

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Author: Chada, Neil K1; Iglesias, Marco A2; Roininen, Lassi3;
Organizations: 1Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom
2School of Mathematical Sciences, University of Nottingham, Nottingham Park, NG7 2QL, United Kingdom
3Department of Mathematical Sciences, University of Oulu, FI-90014, Oulu, Finland
4Computing and Mathematics Sciences, California Institute of Technology, Pasadena, CA 91125, United States of America
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 3.1 MB)
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Language: English
Published: IOP Publishing, 2018
Publish Date: 2019-03-15


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.

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Series: Inverse problems
ISSN: 0266-5611
ISSN-E: 1361-6420
ISSN-L: 0266-5611
Volume: 34
Issue: 5
Article number: 055009
DOI: 10.1088/1361-6420/aab6d9
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Funding: The research of AMS was partially supported by the EPSRC programme grant EQUIP and by AFOSR Grant FA9550-17-1-0185. LR was supported by the EPSRC program grant EQUIP. NKC was partially supported by the EPSRC MASDOC Graduate Training Program and by Premier Oil.
Copyright information: © 2018 IOP Publishing Ltd. This is a peer-reviewed, 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