Imaging of isotropic and anisotropic conductivities from power densities in three dimensions

We present numerical reconstructions of anisotropic conductivity tensors in three dimensions, from knowledge of a finite family of power density functionals. Such a problem arises in the coupled-physics imaging modality ultrasound modulated electrical impedance tomography for instance. We improve on...

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Bibliographic Details
Published in:Inverse problems 2018-07, Vol.34 (7), p.75005
Main Authors: Monard, François, Rim, Donsub
Format: Article
Language:English
Subjects:
conductivity imaging
coupled physics
hybrid imaging
quaternions
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Summary:We present numerical reconstructions of anisotropic conductivity tensors in three dimensions, from knowledge of a finite family of power density functionals. Such a problem arises in the coupled-physics imaging modality ultrasound modulated electrical impedance tomography for instance. We improve on the algorithms previously derived in Bal et al (2013 Inverse Problems Imaging 7 353-75); Monard and Bal (2013 Commun. PDE 38 1183-207) for both isotropic and anisotropic cases, and we address the well-known issue of vanishing determinants in particular. The algorithm is implemented and we provide numerical results that illustrate the improvements.
ISSN:0266-5611
1361-6420
DOI:10.1088/1361-6420/aabe5a