Feasibility of hybrid inverse problems in limited view

TL;DR

This paper investigates the feasibility of reconstructing electrical conductivity in limited view hybrid inverse problems, focusing on boundary function selection to ensure successful reconstructions, supported by theoretical analysis and numerical experiments.

Contribution

It provides a theoretical framework for choosing boundary functions in limited view scenarios to guarantee non-zero Jacobian, enabling feasible reconstructions.

Findings

Boundary function selection is crucial for reconstruction feasibility.

Theoretical conditions for non-zero Jacobian are established.

Numerical reconstructions validate the theoretical approach.

Abstract

Hybrid inverse problems such as Acousto-Electric Tomography, Current Density Imaging or Magnetic Resonance Electric Impedance Tomography are concerned with reconstructing the electrical conductivity from interior measurements. For a two-dimensional object the measurements correspond to two different functions imposed as the Neumann boundary condition to an elliptic PDE. In limited view these functions are only non-zero on the part of the boundary that one can control. In this paper we address how to choose such boundary functions in limited view such that the reconstruction procedure is feasible. This is related to the corresponding Jacobian being non-zero. We supplement the theoretical results by numerical reconstructions following the approach of Acousto-Electric Tomography.