Positive-energy D-bar method for acoustic tomography: a computational study
Numerical Analysis
2016-02-03 v2
Abstract
A new computational method for reconstructing a potential from the Dirichlet-to-Neumann map at positive energy is developed. The method is based on D-bar techniques and it works in absence of exceptional points -- in particular, if the potential is small enough compared to the energy. Numerical tests reveal exceptional points for perturbed, radial potentials. Reconstructions for several potentials are computed using simulated Dirichlet-to-Neumann maps with and without added noise. The new reconstruction method is shown to work well for energy values between and , smaller values giving better results.
Keywords
Cite
@article{arxiv.1307.2037,
title = {Positive-energy D-bar method for acoustic tomography: a computational study},
author = {Maarten de Hoop and Matti Lassas and Matteo Santacesaria and Samuli Siltanen and Janne P. Tamminen},
journal= {arXiv preprint arXiv:1307.2037},
year = {2016}
}