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MUSIC-type imaging of perfectly conducting cracks in limited-view inverse scattering problems.pdf
Applied Mathematics and Computation 240 (2014) 273–280
Contents lists available at ScienceDirect
Applied Mathematics and Computation
journal homepage: /locate/amc
MUSIC-type imaging of perfectly conducting cracks in limited-view inverse scattering problems
Young-Deuk Joh, Young Mi Kwon, Won-Kwang Park ?
Department of Mathematics, Kookmin University, Seoul 136-702, Republic of Korea
article info
Keywords: MUSIC algorithm Perfectly conducting cracks Limited-view inverse scattering Bessel functions Numerical experiments
abstract
Although standard MUltiple SIgnal Classi?cation (MUSIC) algorithm has been considered a promising non-iterative imaging technique for cracks, its application is restricted to the full-view inverse scattering problems. Many experimental results revealed that MUSIC can be applied to the imaging of perfectly conducting cracks with small length in limited-view inverse scattering problem. On the other hand, MUSIC is not applicable for imaging of extended cracks in limited-view problems but the reason behind this restricted application has not been theoretically investigated. This gave an impetus for this study to attempt to identify the structure of MUSIC-type algorithm that appears in the limited-view inverse scattering problems by establishing a relationship between MUSIC and Bessel functions of integer order of the ?rst kind. Some numerical experiments are illustrated to support the identi?ed structure of MUSIC.
ó 2014 Elsevier Inc. All rights reserved.
1. Introduction
Inverse scattering problem for reconstructing the shape of perfectly conducting cracks hidden in a structure (such as a bridge or a concrete wall) is an old problem which, nevertheless, still poses great challenges to nowaday scientists for developing novel tools and techniques which can be applied to this problem because this is closely related to human life, refer to [2,3,6] and references therein. In order to solve this kind of inverse problem, many authors have proposed various
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