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Analysis of subspace migrations in limited-view inverse scattering problems.pdf
Applied Mathematics Letters 26 (2013) 1107–1113
Contents lists available at ScienceDirect
Applied Mathematics Letters
journal homepage: /locate/aml
Analysis of subspace migrations in limited-view inverse scattering problems
Young Mi Kwon, Won-Kwang Park ?
Department of Mathematics, Kookmin University, Seoul, 136-702, Republic of Korea
article info
Article history: Received 18 April 2013 Received in revised form 29 May 2013 Accepted 29 May 2013
Keywords: Subspace migration Limited-view inverse problem Multi-static response (MSR) matrix Bessel functions Numerical examples
abstract
An analysis of subspace migration that occurs in the limited-view inverse scattering problem is considered herein. Based on the structure of singular vectors associated with the nonzero singular values of the multi-static response matrix, we establish a relationship between the subspace migration imaging function and Bessel functions of integer order of the first kind. The revealed structure and numerical examples show why subspace migration is applicable for imaging of small scatterers in limited-view inverse scattering problems.
? 2013 Elsevier Ltd. All rights reserved.
1. Introduction
This work focuses on subspace migration for imaging of small scatterers located in the homogeneous two-dimensional space R2 in limited-view inverse scattering problems. Subspace migration is a simple and effective imaging technique, so it is applied to a lot of inverse scattering problems. For this reason, various remarkable properties have been studied and investigated in much research. Related works can be found in [1–10] and the references therein.
Based on this research, it turns out that subspace migration can be applied not only in full-view but also in limitedview inverse scattering problems. However, the use of the subspace migration-based imaging technique has been applied heuristically. Hence, in [1,4], the structure of subspace migration in full-view inverse scattering problems has been establishe
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