A modified gradient method for two-dimensional problems in tomography
type: Item
instance of: scholarly article
title: A modified gradient method for two-dimensional problems in tomography
zbMATH Open document ID: 0757.65133
DOI: 10.1016/0377-0427(92)90160-Y
published in: Journal of Computational and Applied Mathematics
publication date: 1992-10-26T00:00:00Z
review text: A method for reconstruction of a bounded two-dimensional inhomogeneous object from a measured scattered field is presented. The governing domain integral equation is solved iteratively by a successive overrelaxation technique. Convergence of this process is established for indices of refraction much larger than required for convergence of the Born approximation. Numerical results are presented for a number of representative two-dimensional objects.
reviewed by: Wilhelm Heinrichs
Mathematics Subject Classification ID: 65R10
Mathematics Subject Classification ID: 65R30
Mathematics Subject Classification ID: 44A12
Mathematics Subject Classification ID: 92C55
zbMATH DE Number: 69582
zbMATH Keywords: tomography
zbMATH Keywords: scattering
zbMATH Keywords: gradient method
zbMATH Keywords: two-dimensional
zbMATH Keywords: inverse problem
zbMATH Keywords: profile inversion
zbMATH Keywords: reconstruction
zbMATH Keywords: successive overrelaxation
zbMATH Keywords: Convergence
zbMATH Keywords: Numerical results
Wikidata QID: Q63664764
author: Ralph E. Kleinman
author: Peter M. van den Berg
MaRDI profile type: Publication
cites work: Q3334886
cites work: Q3881429
cites work: An over-relaxation method for the iterative solution of integral equations in scattering problems
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cites work: On a General Iterative Method for the Approximate Solution of Linear Operator Equations
cites work: Q3713481
cites work: Newton-Kantorovitch algorithm applied to an electromagnetic inverse problem
cites work: Iterative inverse scattering method employing Gram-Schmidt orthogonalization
cites work: Inverse scattering in elasticity -- a modified gradient approach
cites work: Q5342712
full work available at URL: 0377-0427(92)90160-y
OpenAlex ID: W1986924342
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description: scientific article; zbMATH DE number 69582