Imaging of isotropic and anisotropic conductivities from power densities in three dimensions
For researchers in coupled-physics imaging, this work incrementally improves existing algorithms for conductivity reconstruction.
The paper presents improved numerical reconstruction algorithms for anisotropic conductivity tensors from power density measurements in 3D, addressing the issue of vanishing determinants, with numerical results demonstrating the improvements.
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.