A new computational method for reconstructing a potential from the Dirichlet-to-Neumann (DN) 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 DN 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.
Positive-energy D-bar method for acoustic tomography: A computational study
Matteo Santacesaria;
2016-01-01
Abstract
A new computational method for reconstructing a potential from the Dirichlet-to-Neumann (DN) 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 DN 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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