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arXiv · 1307.2037

Positive-energy D-bar method for acoustic tomography: a computational study

Maarten de Hoop·Matti Lassas·Matteo Santacesaria·Samuli Siltanen·Janne P. Tamminen
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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 $10^{-5}$ and $5$, smaller values giving better results.

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Maarten de Hoop, Matti Lassas, Matteo Santacesaria, Samuli Siltanen, Janne P. Tamminen. 2013-07-08. Positive-energy D-bar method for acoustic tomography: a computational study. https://doi.org/10.1088/0266-5611%2F32%2F2%2F025003

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