Regularized quasi-Newton method for inverse scattering problems
type: Item
instance of: scholarly article
title: Regularized quasi-Newton method for inverse scattering problems
zbMATH Open document ID: 0788.65125
DOI: 10.1016/0895-7177(93)90076-B
published in: Mathematical and Computer Modelling
publication date: 1994-05-30T00:00:00Z
review text: The problem is how to extract the properties of the medium from the information contained in the measurements, assuming that the frequency is known and it is constant. The weak scattering case is considered, that is the unknown spatial variations of the medium are assumed to be close to zero. The authors work directly with the Helmholtz differential equation. Compared to usual numerical methods based on the Lippman-Schwinger integral equation this approach is quite different computationally. The iterative algorithm is a regularized quasi-Newton method. The linearized (Born) approximation is the first iteration and further iterations improve the identification by an order of magnitude. A special regularization of the Fréchet derivative's inverse provides a significant improvement in the algorithm's performance. The parameter identification for noisy data is also discussed. The algorithm is tested numerically in the 2D case for scattering from two coaxial cylinders. The mathematical framework covers also the 3D case.
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 81U40
zbMATH DE Number: 474542
zbMATH Keywords: inverse scattering
zbMATH Keywords: numerical examples
zbMATH Keywords: weak scattering
zbMATH Keywords: Helmholtz differential equation
zbMATH Keywords: Lippman-Schwinger integral equation
zbMATH Keywords: iterative algorithm
zbMATH Keywords: regularized quasi-Newton method
zbMATH Keywords: parameter identification
author: Semion Gutman
author: Michael V. Klibanov
reviewed by: Viorel Arnăutu
MaRDI profile type: Publication
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full work available at URL: 0895-7177(93)90076-b
OpenAlex ID: W1989480281
description: scientific article; zbMATH DE number 474542