Recovering the conductivity from a single measurement of interior data

Abstract

We consider the problem of recovering the conductivity of an object from knowledge of the magnitude of one current density field in its interior. A known voltage potential is assumed imposed at the boundary. We prove identifiability and propose an iterative reconstruction procedure. The computational feasibility of this procedure is demonstrated in some numerical experiments.

Ultrasound Modulated Bioluminescence Tomography and Controllability of the Radiative Transport Equation

“…In this manner, the above inverse source problem is converted into a so-called hybrid inverse problem, where an external field is used to control the material properties of a medium of interest, which is then probed by a second field. See [3,4,5,6,7,8,9,10,13,19,21,22,24,25,26,27] for examples of hybrid inverse problems in other physical settings.…”

Inverse Scattering and Acousto-Optic Imaging

“…Once the c k are found, we can then recover 0 and D 0 from (32) and (33), which yields the solution to the nonlinear inverse problem of AOI.…”

“…The case p ¼ 0 was also addressed in [31,32] in a different physical context and solved numerically using an iterative algorithm similar to the fixed point algorithm presented in (22). The case p ¼ 1 was studied in [33], where uniqueness results and numerical methods were described. See also related work in [34].…”

Enclosure method for the p -Laplace equation

“…The n-Laplacian is used in conformal geometry [40]. The formal 0-Laplacian is used in ultrasound mediated EIT [1,7,8,20] and the formal 1-Laplacian in conductivity density imaging [26,35,37,42,53]. The limiting case p = ∞ is also of mathematical interest [17].…”