A Bayesian approach to improving the Born approximation for inverse scattering with high contrast materials

Time harmonic inverse scattering using accurate forward models is often computationally expensive. On the other hand, the use of computationally efficient solvers, such as the Born approximation, may fail if the targets do not satisfy the assumptions of the simplified model. In the Bayesian framewor...

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Bibliographic Details
Published in:arXiv.org 2019-07
Main Authors: Kaipio, Jari P, Huttunen, Tomi, Luostari, Teemu, Lähivaara, Timo, Monk, Peter B
Format: Article
Language:English
Subjects:
Approximation
Bayesian analysis
Born approximation
Error analysis
Far fields
Inverse problems
Inverse scattering
Mathematical analysis
Refractivity
Solvers
Statistical models
Online Access:Get full text
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Summary:Time harmonic inverse scattering using accurate forward models is often computationally expensive. On the other hand, the use of computationally efficient solvers, such as the Born approximation, may fail if the targets do not satisfy the assumptions of the simplified model. In the Bayesian framework for inverse problems, one can construct a statistical model for the errors that are induced when approximate solvers are used, and hence increase the domain of applicability of the approximate model. In this paper, we investigate the error structure that is induced by the Born approximation and show that the Bayesian approximation error approach can be used to partially recover from these errors. In particular, we study the model problem of reconstruction of the index of refraction of a penetrable medium from measurements of the far field pattern of the scattered wave.
ISSN:2331-8422
DOI:10.48550/arxiv.1901.00909