Analysis of MUSIC-type imaging functional for single, thin electromagnetic inhomogeneity in limited-view inverse scattering problem.pdfVIP

Analysis of MUSIC-type imaging functional for single, thin electromagnetic inhomogeneity in limited-view inverse scattering problem.pdf

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Analysis of MUSIC-type imaging functional for single, thin electromagnetic inhomogeneity in limited-view inverse scattering problem.pdf

Journal of Computational Physics 291 (2015) 198–217 Contents lists available at ScienceDirect Journal of Computational Physics /locate/jcp Analysis of MUSIC-type imaging functional for single, thin electromagnetic inhomogeneity in limited-view inverse scattering problem Chi Young Ahn a, Kiwan Jeon a, Won-Kwang Park b,? a National Institute for Mathematical Sciences, Daejeon, 305-811, Republic of Korea b Department of Mathematics, Kookmin University, Seoul, 136-702, Republic of Korea article info Article history: Received 7 November 2014 Received in revised form 3 March 2015 Accepted 5 March 2015 Available online 17 March 2015 Keywords: Limited-view inverse scattering problem MUltiple SIgnal Classi?cation (MUSIC) Thin electromagnetic inhomogeneity Bessel functions Numerical simulation abstract This study analyzes the well-known MUltiple SIgnal Classi?cation (MUSIC) algorithm to identify unknown support of thin penetrable electromagnetic inhomogeneity from scattered ?eld data collected within the so-called multi-static response matrix in limitedview inverse scattering problems. The mathematical theories of MUSIC are partially discovered, e.g., in the full-view problem, for an unknown target of dielectric contrast or a perfectly conducting crack with the Dirichlet boundary condition (Transverse Magnetic– TM polarization) and so on. Hence, we perform further research to analyze the MUSICtype imaging functional and to certify some well-known but theoretically unexplained phenomena. For this purpose, we establish a relationship between the MUSIC imaging functional and an in?nite series of Bessel functions of integer order of the ?rst kind. This relationship is based on the rigorous asymptotic expansion formula in the existence of a thin inhomogeneity with a smooth supporting curve. Various results of numerical simulation are presented in order to support the identi?ed structure of MUSIC. Although a priori information of the target is needed, we suggest a least condition o

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