Imaging of isotropic and anisotropic conductivities from power densities in three dimensions. (14th May 2018)

• Record Type: Journal Article
• Authors: Monard, François; Rim, Donsub
• Is Part Of: Inverse problems. Volume 34:Number 7(2018:Jul.)
• Publication Date: 2018-05-14
• Subjects: hybrid imaging -- conductivity imaging -- coupled physics -- quaternions; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aabe5a
• Languages: English
• ISSNs: 0266-5611

Abstract

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 (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.