Inverse Scattering Related to Cylindrical Bodies Buried in a Lossy Circular Cylinder with Resistive Boundary

Frequenz ◽  
2019 ◽  
Vol 73 (3-4) ◽  
pp. 1-9 ◽  
Author(s):  
Tanju Yelkenci
Keyword(s):  
Circular Cylinder ◽  
Plane Wave ◽  
Cross Section ◽  
Inverse Scattering ◽  
Scattered Field ◽  
Born Approximation ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Field Measurements ◽  
Arbitrary Cross Section

Abstract An inverse scattering problem of cylindrical bodies of arbitrary cross section buried in a circular cylinder with resistive boundary is presented. The reconstruction is obtained from the scattered field measurements for a plane wave illumination under the Born approximation. Illustrative examples are presented in order to see the applicability of the method as well as to see the effects of some parameters on the solution.

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.

Approximate solution of nonlinear double-scattering inversion for true amplitude imaging

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. R43-R55 ◽  
Author(s):  
Wei Ouyang ◽  
Weijian Mao ◽  
Xuelei Li
Keyword(s):  
Scattered Field ◽  
Born Approximation ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Single Scattering ◽  
Complex Model ◽  
Earth Model ◽  
Model Parameters ◽  
Double Scattering ◽  
Integral Equation Formulation

Linearized inversion algorithms are the main techniques in seismic imaging that apply the single-scattering (Born) approximation to the scattered field, and therefore, have difficulty handling the strong perturbation of model parameters and nonlinear multiple-scattering effects. To theoretically overcome these drawbacks in the linearization of the inverse scattering problem, we have developed an approach to deal with nonlinear double-scattering inversion. We first used an integral equation formulation associated with the scattered field consisting of single and double scattering in an acoustic earth model based on the second-order Born approximation, and we found that the approximation of the scattered field can be naturally related to the generalized Radon transform (GRT). We then adopted the inverse GRT to obtain the corresponding quadratic approximate inversion solution. Our inversion scheme can appropriately handle the first-order transmission effects from double scattering in a local area, which gives a significant amplitude correction for the inversion results and ultimately results in a more accurate image with true amplitude. We conducted numerical experiments that showed the conventional single-scattering inversion was good in amplitude only for perturbation up to 10% of the background medium, but our approach can work for up to 40% or more. Test results indicated that our inversion scheme can effectively relax the requirement of the weak perturbation of the model parameter in the Born approximation and can deal with the complex model directly. The computational complexity of our new scheme is almost the same as conventional linear scattering inversion processing. Therefore, the cost of our approach is at a similar level to that of linear scattering inversion.

scholarly journals Through-the-Wall Microwave Imaging: Forward and Inverse Scattering Modeling

Sensors ◽  
2020 ◽  
Vol 20 (10) ◽  
pp. 2865 ◽  
Author(s):  
Alessandro Fedeli ◽  
Matteo Pastorino ◽  
Cristina Ponti ◽  
Andrea Randazzo ◽  
Giuseppe Schettini
Keyword(s):  
Electromagnetic Field ◽  
Inverse Scattering ◽  
Scattered Field ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Microwave Imaging ◽  
Numerical Results ◽  
Lebesgue Spaces ◽  
Non Linear ◽  
Inversion Procedure

The imaging of dielectric targets hidden behind a wall is addressed in this paper. An analytical solver for a fast and accurate computation of the forward scattered field by the targets is proposed, which takes into account all the interactions of the electromagnetic field with the interfaces of the wall. Furthermore, an inversion procedure able to address the full underlying non-linear inverse scattering problem is introduced. This technique exploits a regularizing scheme in Lebesgue spaces in order to reconstruct an image of the hidden targets. Preliminary numerical results are provided in order to initially assess the capabilities of the developed solvers.

Stable methods for solving the inverse scattering problem for a cylinder

1981 ◽  
Vol 89 (3-4) ◽  
pp. 181-188 ◽  
Author(s):  
David Colton ◽  
Andreas Kirsch
Keyword(s):  
Cross Section ◽  
Inverse Scattering ◽  
Scattering Problem ◽  
Plane Waves ◽  
Inverse Scattering Problem ◽  
Initial Approximation ◽  
Constructive Method ◽  
Infinite Cylinder ◽  
Unknown Boundary ◽  
Closed Curves

SynopsisIt is shown that the inverse scattering problem for an infinite cylinder can be stabilized by assuming a priori that the unknown boundary of the cylindrical cross section lies in a compact family of continuously differentiable simple closed curves. A constructive method for determining the shape of this boundary is given under the assumption that an initial approximation is known and that the scattering cross section is known forn distinct incoming plane waves in the resonant region.

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