Inverse Scattering In The First Born Approximation

1982 ◽  
Author(s):  
William H. Carter
Keyword(s):  
Inverse Scattering ◽  
Born Approximation

TWO VERSIONS OF QUASI-NEWTON METHOD FOR MULTIDIMENSIONAL INVERSE SCATTERING PROBLEM

1993 ◽  
Vol 01 (02) ◽  
pp. 197-228 ◽  
Author(s):  
SEMION GUTMAN ◽  
MICHAEL KLIBANOV
Keyword(s):  
Newton Method ◽  
Inverse Scattering ◽  
Born Approximation ◽  
Scattering Problem ◽  
Plane Waves ◽  
Inverse Scattering Problem ◽  
Circular Cylinders ◽  
Iterative Sequence ◽  
Scattering Field ◽  
Quasi Newton

Suppose that a medium with slowly changing spatial properties is enclosed in a bounded 3-dimensional domain and is subjected to a scattering by plane waves of a fixed frequency. Let measurements of the wave scattering field induced by this medium be available in the region outside of this domain. We study how to extract the properties of the medium from the information contained in the measurements. We are concerned with the weak scattering case of the above inverse scattering problem (ISP), that is, the unknown. spatial variations of the medium are assumed to be close to a constant. Examples can be found in the studies of the wave propagation in oceans, in the atmosphere, and in some biological media. Since the problems are nonlinear, the methods for their linearization (the Born approximation) have been developed. However, such an approach often does not produce good results. In our method, the Born approximation is just the first iteration and further iterations improve the identification by an order of magnitude. The iterative sequence is defined in the framework of a Quasi-Newton method. Using the measurements of the scattering field from a carefully chosen set of directions we are able to recover (finitely many) Fourier coefficients of the sought parameters of the model. Numerical experiments for the scattering from coaxial circular cylinders as well as for simulated data are presented.

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

2019 ◽  
Vol 35 (8) ◽  
pp. 084001 ◽  
Author(s):  
J P Kaipio ◽  
T Huttunen ◽  
T Luostari ◽  
T Lähivaara ◽  
P B Monk
Keyword(s):  
Inverse Scattering ◽  
Bayesian Approach ◽  
Born Approximation ◽  
High Contrast ◽  
Contrast Materials

Impact of the Born approximation on the estimation error in 2D inverse scattering

2016 ◽  
Vol 32 (6) ◽  
pp. 065006 ◽  
Author(s):  
M L Diong ◽  
A Roueff ◽  
P Lasaygues ◽  
A Litman
Keyword(s):  
Inverse Scattering ◽  
Born Approximation ◽  
Estimation Error
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