English

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 10510^{-5} and 55, 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}
}
R2 v1 2026-06-22T00:47:21.442Z