Positive-energy D-bar method for acoustic tomography: a computational study. (11th January 2016)

• Record Type: Journal Article
• Authors: Hoop, M V de; Lassas, M; Santacesaria, M; Siltanen, S; Tamminen, J P
• Is Part Of: Inverse problems. Volume 32:Number 2(2016:Feb.)
• Publication Date: 2016-01-11
• Subjects: acoustic tomography -- geophysical prospecting -- reconstruction algorithm -- non-local Riemann–Hilbert problem -- D-bar equation -- Dirichlet-to-Neumann map -- exceptional points; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/2/025003
• Languages: English
• ISSNs: 0266-5611

Abstract

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.