The D-Bar Method for Diffuse Optical Tomography: A Computational Study

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 diffuse optical tomography, a new way of reconstructing the diffusion coefficient from the associated Complex Geometrics Optics solution is suggested and numerically validated.

KEYWORDS:

• inverse problems
• diffuse optical tomography
• D-bar method
• numerical simulation
• exceptional points

2000 AMS SUBJECT CLASSIFICATION:

• 35R30

Funding

This work has been supported by the Academy of Finland (projects 136220, 272803, and 250215 Finnish Centre of Excellence in Inverse Problems Research). JPT was supported in part by the Finnish Cultural Foundation and European Research Council (ERC).