Inverse scattering by point-like scatterers in the Foldy regime

@article{Challa2012InverseSB,
  title={Inverse scattering by point-like scatterers in the Foldy regime},
  author={Durga Prasad Challa and Mourad Sini},
  journal={Inverse Problems},
  year={2012},
  volume={28}
}
The scattering by point-like scatterers is described in the Born, Foldy and the intermediate regimes. We explain why the Foldy regime is, rigorously, a natural model for taking into account the multiple scattering. For each regime, we study the inverse problems for detecting these scatterers as well as the scattering strengths. In the first part, we do it for the acoustic case, and in the second, we study the corresponding models for the linearized isotropic elastic case. In this last case, we… 
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References

SHOWING 1-10 OF 28 REFERENCES
On the far‐field operator in elastic obstacle scattering
We investigate the far-field operator for the scattering of time-harmonic elastic plane waves by either a rigid body, a cavity, or an absorbing obstacle. Extending results of Colton & Kress for
The Multiple Scattering of Waves. I. General Theory of Isotropic Scattering by Randomly Distributed Scatterers
While the problem of the multiple scattering of particles by a random distribution of scatterers has been treated classically through the use of the Boltzmann integro-differential equation, the
On the scattering amplitudes for elastic waves
Reciprocity and scattering theorems for the normalized spherical scattering amplitude for elastic waves are obtained for the case of a rigid scatterer, a cavity and a penetrable scattering region.
Elastic scattering by finitely many point-like obstacles
This paper is concerned with the time-harmonic elastic scattering by a finite number N of point-like obstacles in Rn (n = 2, 3). We analyze the N-point interactions model in elasticity and derive the
AN INVERSE PROBLEM FOR POINT INHOMOGENEITIES
We study quantum scattering theory off n point inhomogeneities (n 2 N) in three dimensions. The inhomogeneities (or generalized point inter- actions) positioned at {�1,...,�n} � R 3 are modeled in
Identification of obstacles using only the scattered P-waves or the scattered S-waves
In this work, we are concerned with the inverse scattering by obstacles for the linearized, homogeneous and isotropic elastic model. We study the uniqueness issue of detecting smooth obstacles from
Multiple Scattering
The purpose of this work is to find the time dependent distributions of directions and positions of a particle that undergoes multiple elastic scattering. The angular cross section is given and the
An analytical approach to estimate the number of small scatterers in 2D inverse scattering problems
This paper presents an analytical method to estimate the location and number of actual small targets in 2D inverse scattering problems. This method is motivated from the exact maximum likelihood
Noniterative analytical formula for inverse scattering of multiply scattering point targets.
TLDR
A noniterative analytical formula for the nonlinear inversion of the target scattering strengths from the scattering or response matrix that can be applied after the target positions have been estimated in a previous step via, e.g., time-reversal multiple signal classification or another approach.
Time-reversal-based imaging and inverse scattering of multiply scattering point targets
The treatment of time-reversal imaging of multiply scattering point targets developed by the present authors in Gruber et al. [“Time-reversal imaging with multiple signal classification considering
...
...