Results 1  10
of
24
A Regularized Sampling Method for Solving Three Dimensional Inverse Scattering Problems
 SIAM J. Sci. Comput
, 2000
"... The inverse scattering problem under consideration is to determine the shape of an obstacle in R³ from a knowledge of the time harmonic incident acoustic wave and the far field pattern of the scattered wave with frequency in the resonance region. A method for solving this nonlinear and impr ..."
Abstract

Cited by 16 (2 self)
 Add to MetaCart
(Show Context)
The inverse scattering problem under consideration is to determine the shape of an obstacle in R&sup3; from a knowledge of the time harmonic incident acoustic wave and the far field pattern of the scattered wave with frequency in the resonance region. A method for solving this nonlinear and improperly posed problem is presented which is based on solving a linear integral equation of the first kind and avoids the use of nonlinear optimization methods. Numerical examples are given showing the practicality of this new approach.
A Time Domain Point Source Method for Inverse Scattering by Rough Surfaces
"... In this paper we propose a new method to determine the location and shape of an unbounded rough surface from measurements of scattered electromagnetic waves. The proposed method is based on the point source method of Potthast (IMA J.Appl.Math., 61:119140, 1998) for inverse scattering by bounded obs ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
(Show Context)
In this paper we propose a new method to determine the location and shape of an unbounded rough surface from measurements of scattered electromagnetic waves. The proposed method is based on the point source method of Potthast (IMA J.Appl.Math., 61:119140, 1998) for inverse scattering by bounded obstacles. We propose a version for inverse rough surface scattering which can reconstruct the total field when the incident field is not necessarily time harmonic. We present numerical results for the case of a perfectly conducting surface in TE polarization, in which case a homogeneous Dirichlet condition applies on the boundary. The results show great accuracy of reconstruction of the total field and of the prediction of the surface location. 1
Multifrequency Inverse Obstacle Scattering . . .
, 2003
"... This work is a study of strategies for obstacle reconstruction from multifrequency far field scattering data. We outline two strategies for obstacle reconstruction from multifrequency far field scattering data: the point source method proposed by Potthast for solving inverse scattering problems with ..."
Abstract

Cited by 6 (5 self)
 Add to MetaCart
This work is a study of strategies for obstacle reconstruction from multifrequency far field scattering data. We outline two strategies for obstacle reconstruction from multifrequency far field scattering data: the point source method proposed by Potthast for solving inverse scattering problems with single frequency data in the resonance region, and filtered backprojection techniques based on the physical optics approximation for high frequency scattering. Our implementation of the point source method can be viewed as a generalized filtered backprojection algorithm, the key to which is the construction of the filter used in the backprojection operator. Numerical examples indicate that the critical factor for reconstructions in multifrequency settings is the frequency dependence of the filter.
Inverse crack problem and probe method
 Cubo
, 2006
"... A problem of extracting information about the location and shape of unknown cracks in a background medium from the DirichlettoNeumann map is considered. An application of a new formulation of the probe method introduced by the author to the problem is given. The method is based on: the blowup prop ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
(Show Context)
A problem of extracting information about the location and shape of unknown cracks in a background medium from the DirichlettoNeumann map is considered. An application of a new formulation of the probe method introduced by the author to the problem is given. The method is based on: the blowup property of sequences of special solutions of the governing equation for the background medium which are related to a singular solution of the equation; an explicit lower bound of an L2norm of the gradient of the socalled reflected solution. AMS: 35R30
Image synthesis for inverse obstacle scattering using the eigenfunction expansion theorem
 Computing
, 2005
"... In recent years several new inverse scattering techniques have been developed that determine the boundary of an unknown obstacle by reconstructing the surrounding scattered field. In the case of sound soft obstacles, the boundary is usually found as the minimum contour of the total field. In this no ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
(Show Context)
In recent years several new inverse scattering techniques have been developed that determine the boundary of an unknown obstacle by reconstructing the surrounding scattered field. In the case of sound soft obstacles, the boundary is usually found as the minimum contour of the total field. In this note we derive a different approach for imaging the boundary from the reconstructed fields based on a generalization of the eigenfunction expansion theorem. The aim of this alternative approach is the construction of higher contrast images than is currently obtained with the minimum contour approach. AMS Subject Classification: 35R30, 35P25, 68U10, 94A08 Key words: inverse problems, scattering theory, image processing, eigenfunction expansion
Two sides of probe method and obstacle with impedance boundary condition
 Hokkaido Math. J
"... ..."
(Show Context)
On Source Analysis by Wave Splitting with Applications in Inverse Scattering of Multiple Obstacles
, 2006
"... We study wave splitting procedures for acoustic or electromagnetic scattering problems. The idea of these procedures is to split some scattered field into a sum of fields coming from different spatial regions such that this information can be used either for inversion algorithms or for active noise ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
We study wave splitting procedures for acoustic or electromagnetic scattering problems. The idea of these procedures is to split some scattered field into a sum of fields coming from different spatial regions such that this information can be used either for inversion algorithms or for active noise control. Splitting algorithms can be based on general boundary layer potential representation or Green’s representation formula. We will prove the unique decomposition of scattered wave outside the specified reference domain G and the unique decomposition of farfield pattern with respect to different reference domain G. Further, we employ the splitting technique for field reconstruction for a scatterer with two or more separate components, by combining it with the point source method for wave recovery. Using the decomposition of scattered wave as well as its farfield pattern, the wave splitting procedure proposed in this paper gives an efficient way to the computation of scattered wave near the obstacle, from which the multiple obstacles which cause the farfield pattern can be reconstructed separately. This considerably extends the range of the decomposition methods in the area of inverse scattering. Finally, we will provide numerical examples to prove the feasibility of the splitting method.
The Point Source Method in Inverse Acoustic Scattering, MSc Dissertation, The University of Reading 2004
"... We pose the direct and inverse problems in acoustic scattering, both informally and mathematically, and detail a method for computing the solution to the direct problem. We present the point source method of R. Potthast as a way to solve the inverse problem for a soundsoft scatterer, which is shown ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
We pose the direct and inverse problems in acoustic scattering, both informally and mathematically, and detail a method for computing the solution to the direct problem. We present the point source method of R. Potthast as a way to solve the inverse problem for a soundsoft scatterer, which is shown to be illposed. A thorough account of the method is given, as well as an error analysis, before detailing a method for its successful implementation in two dimensions. We briefly describe the technique of Tikhonov regularisation as a means of finding solutions to illposed problems, and its implementation in the solution of the inverse problem. We include numerical results for the solution of both the direct and inverse problems in two dimensions. Declaration I confirm that this is my own work, and the use of all material from other sources has been properly and fully acknowledged.
ReducedBasis Approximations and A Posteriori Error Bound for Nonaffine and Nonlinear Partial Differential Equations: Application to Inverse Analysis
, 2005
"... ..."