A1 Journal article (refereed)
Jacobian of solutions to the conductivity equation in limited view (2022)

Salo, M., & Schlüter, H. (2022). Jacobian of solutions to the conductivity equation in limited view. Inverse Problems, 39(2), Article 025001. https://doi.org/10.1088/1361-6420/aca904

JYU authors or editors

Publication details

All authors or editors: Salo, Mikko; Schlüter, Hjørdis

Journal or series: Inverse Problems

ISSN: 0266-5611

eISSN: 1361-6420

Publication year: 2022

Publication date: 06/12/2022

Volume: 39

Issue number: 2

Article number: 025001

Publisher: IOP Publishing

Publication country: United Kingdom

Publication language: English

DOI: https://doi.org/10.1088/1361-6420/aca904

Publication open access: Not open

Publication channel open access: Channel is not openly available

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/84615

Web address of parallel published publication (pre-print): https://arxiv.org/abs/2207.03849

Abstract

The aim of hybrid inverse problems such as Acousto-Electric Tomography or Current Density Imaging is the reconstruction of the electrical conductivity in a domain that can only be accessed from its exterior. In the inversion procedure, the solutions to the conductivity equation play a central role. In particular, it is important that the Jacobian of the solutions is non-vanishing. In the present paper we address a two-dimensional limited view setting, where only a part of the boundary of the domain can be controlled by a non-zero Dirichlet condition, while on the remaining boundary there is a zero Dirichlet condition. For this setting, we propose sufficient conditions on the boundary functions so that the Jacobian of the corresponding solutions is non-vanishing. In that regard we allow for discontinuous boundary functions, which requires the use of solutions in weighted Sobolev spaces. We implement the procedure of reconstructing a conductivity from power density data numerically and investigate how this limited view setting affects the Jacobian and the quality of the reconstructions.

Keywords: inverse problems

Free keywords: acousto-electric tomography; current density imaging; hybrid inverse problems; coupled physics imaging; non-vanishing Jacobian; conductivity equation

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Ministry reporting: Yes

Reporting Year: 2022

JUFO rating: 2