1. Modified forward and inverse Born series for the Calderon and diffuse-wave problems
- Author
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Marc Bonnet, Shari Moskow, Anuj Abhishek, Department of mathematics [Philadelphie], Drexel University, Propagation des Ondes : Étude Mathématique et Simulation (POEMS), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Unité de Mathématiques Appliquées (UMA), and École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-Centre National de la Recherche Scientifique (CNRS) more...
- Subjects
Series (mathematics) ,Applied Mathematics ,Mathematical analysis ,Inverse ,010103 numerical & computational mathematics ,Radius ,Born series ,[INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation ,01 natural sciences ,Computer Science Applications ,Theoretical Computer Science ,010101 applied mathematics ,Signal Processing ,Inverse scattering problem ,Convergence (routing) ,Radius of convergence ,0101 mathematics ,Electrical impedance tomography ,Mathematical Physics ,Mathematics - Abstract
We propose a new direct reconstruction method based on series inversion for electrical impedance tomography (EIT) and the inverse scattering problem for diffuse waves. The standard Born series for the forward problem has the limitation that the series requires that the contrast lies within a certain radius for convergence. Here, we instead propose a modified Born series which converges for the forward problem unconditionally. We then invert this modified Born series and compare reconstructions with the usual inverse Born series. We also show that the modified inverse Born series has a larger radius of convergence. more...
- Published
- 2020
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