A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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-tekijät tai -toimittajat

Salo, Mikko

Julkaisun tiedot

Julkaisun kaikki tekijät tai toimittajat: Salo, Mikko; Schlüter, Hjørdis

Lehti tai sarja: Inverse Problems

ISSN: 0266-5611

eISSN: 1361-6420

Julkaisuvuosi: 2022

Ilmestymispäivä: 06.12.2022

Volyymi: 39

Lehden numero: 2

Artikkelinumero: 025001

Kustantaja: IOP Publishing

Julkaisumaa: Britannia

Julkaisun kieli: englanti

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

Julkaisun avoin saatavuus: Ei avoin

Julkaisukanavan avoin saatavuus: Julkaisukanava ei ole avoin

Julkaisu on rinnakkaistallennettu (JYX): https://jyx.jyu.fi/handle/123456789/84615

Rinnakkaistallenteen verkko-osoite (pre-print): https://arxiv.org/abs/2207.03849

Tiivistelmä

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.

YSO-asiasanat: inversio-ongelmat

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

Liittyvät organisaatiot

Hankkeet, joissa julkaisu on tehty

OKM-raportointi: Kyllä

Raportointivuosi: 2022

JUFO-taso: 2