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

Abstract

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, Inverse Probl Imaging (2013), pp.353-375, Monard and Bal, Comm. PDE (2013), pp.1183-1207] 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.

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• A Second Order Non-Smooth Variational Model for Restoring Manifold-Valued Images
• Critical Points for Elliptic Equations with Prescribed Boundary Conditions
• Stable determination of a Lamé coefficient by one internal measurement of displacement

Cited by in corpus (1)

• Acousto-Electric Tomography with Total Variation Regularization