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Representation and reconstruction of covariance operators in linear inverse problems

Lila, E; Arridge, S; Aston, JAD; (2020) Representation and reconstruction of covariance operators in linear inverse problems. Inverse Problems 10.1088/1361-6420/ab8713. (In press). Green open access

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Abstract

We introduce a framework for the reconstruction and representation of functions in a setting where these objects cannot be fully observed, but only indirect and noisy measurements are available, namely an inverse problem setting. The proposed methodology can be applied either to the analysis of indirectly observed functional images or to the associated covariance operators, representing second-order information, and thus lying on a non-Euclidean space. To deal with the ill-posedness of the inverse problem, we exploit the spatial structure of the sample data by introducing a flexible regularizing term embedded in the model. Thanks to its efficiency, the proposed model is applied to MEG data, leading to a novel approach to the investigation of functional connectivity.

Type: Article
Title: Representation and reconstruction of covariance operators in linear inverse problems
Open access status: An open access version is available from UCL Discovery
DOI: 10.1088/1361-6420/ab8713
Publisher version: https://doi.org/10.1088/1361-6420/ab8713
Language: English
Additional information: As the Version of Record of this article is going to be/has been published on a gold open access basis under a CC BY 3.0 licence, this Accepted Manuscript is available for reuse under a CC BY 3.0 licence immediately.
Keywords: stat.ME, stat.ME, stat.AP
UCL classification: UCL
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: https://discovery.ucl.ac.uk/id/eprint/10095880
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