The D-bar Method for Diffuse Optical Tomography: a computational study

TL;DR

This paper implements the D-bar method at negative energy for diffuse optical tomography, enabling potential reconstruction and investigation of exceptional points, and introduces a new reconstruction approach for the diffusion coefficient validated through numerical experiments.

Contribution

The paper introduces a numerical implementation of the D-bar method at negative energy for diffuse optical tomography, including a novel reconstruction technique for the diffusion coefficient.

Findings

Successful numerical reconstruction of potentials.

Identification of exceptional points at negative energy.

Validation of the new diffusion coefficient reconstruction method.

Abstract

The D-bar method at negative energy is numerically implemented. Using the method we are able to numerically reconstruct potentials and investigate exceptional points at negative energy. Subsequently, applying the method to Diffusive Optical Tomography, a new way of reconstructing the diffusion coefficient from the associated Complex Geometrics Optics solution is suggested and numerically validated.