@article {14057,
title = {Two methods for solving a 3D acoustic inverse scattering problem},
journal = {The Journal of the Acoustical Society of America},
volume = {113},
year = {2003},
month = {2003///},
pages = {2191 - 2191},
abstract = {We consider the problem of finding the refractive index of a buried object by using far-field measurements in an inhomogeneous medium. We describe two methods for solving the inverse problem. Both methods are implemented in two steps in order to better deal with the ill-posedness of the problem. In the first method an integral equation of the first kind is derived for the far-field operator which is solved via least-squares and Tikhonov regularization. We then use the solution of the integral equation to derive an over-posed boundary value problem, i.e., the Helmholtz equation in a bounded domain with Cauchy data on the boundary. The index that satisfies this over-posed problem most closely is obtained via the Levenberg{\textendash}Marquardt algorithm. The second method is an iterative method and is based on the Lippmann{\textendash}Schwinger equation. It is implemented via the Newton method. The first step consists, as for the other method. Here we use a Fourier integral approach and regularization via discretization. The second step is to obtain the index by iterating the Lippmann{\textendash}Schwinger equation starting with the Born approximation.},
url = {http://link.aip.org/link/?JAS/113/2191/5},
author = {Seydou,Fadoulourahmane and Gumerov, Nail A. and Duraiswami, Ramani}
}