# American Institue of Mathematical Sciences

• Previous Article
Well-posedness and convergence rates for sparse regularization with sublinear $l^q$ penalty term
• IPI Home
• This Issue
• Next Article
Wave splitting of Maxwell's equations with anisotropic heterogeneous constitutive relations
2009, 3(3): 389-403. doi: 10.3934/ipi.2009.3.389

## Reciprocity gap music imaging for an inverse scattering problem in two-layered media

 1 Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716, United States

Received  March 2009 Revised  May 2009 Published  July 2009

In this work we consider a modified MUSIC method for determining the positions of a collection of small perfectly conducting buried objects from measurements of time-harmonic electromagnetic fields on the surface of ground. This method is based on an asymptotic analysis of certain integrals of electric and magnetic fields, so-called reciprocity gap functionals, as the buried objects shrink to points. Unlike standard MUSIC reconstruction methods our algorithm avoids the computation of the Green's function for the background medium during the reconstruction process, but on the other hand it requires more measurement data. After describing the theoretical foundation of this reconstruction method, we provide numerical results showing its performance. We also compare these results to reconstructions obtained by a standard MUSIC algorithm.
Citation: Roland Griesmaier. Reciprocity gap music imaging for an inverse scattering problem in two-layered media. Inverse Problems & Imaging, 2009, 3 (3) : 389-403. doi: 10.3934/ipi.2009.3.389
 [1] Peter Monk, Jiguang Sun. Inverse scattering using finite elements and gap reciprocity. Inverse Problems & Imaging, 2007, 1 (4) : 643-660. doi: 10.3934/ipi.2007.1.643 [2] Yue-Jun Peng, Shu Wang. Asymptotic expansions in two-fluid compressible Euler-Maxwell equations with small parameters. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1/2) : 415-433. doi: 10.3934/dcds.2009.23.415 [3] Peter C. Gibson. On the measurement operator for scattering in layered media. Inverse Problems & Imaging, 2017, 11 (1) : 87-97. doi: 10.3934/ipi.2017005 [4] Jiann-Sheng Jiang, Chi-Kun Lin, Chi-Hua Liu. Homogenization of the Maxwell's system for conducting media. Discrete & Continuous Dynamical Systems - B, 2008, 10 (1) : 91-107. doi: 10.3934/dcdsb.2008.10.91 [5] Fang Zeng, Xiaodong Liu, Jiguang Sun, Liwei Xu. The reciprocity gap method for a cavity in an inhomogeneous medium. Inverse Problems & Imaging, 2016, 10 (3) : 855-868. doi: 10.3934/ipi.2016024 [6] Christodoulos E. Athanasiadis, Vassilios Sevroglou, Konstantinos I. Skourogiannis. The inverse electromagnetic scattering problem by a mixed impedance screen in chiral media. Inverse Problems & Imaging, 2015, 9 (4) : 951-970. doi: 10.3934/ipi.2015.9.951 [7] Dina Kalinichenko, Volker Reitmann, Sergey Skopinov. Asymptotic behavior of solutions to a coupled system of Maxwell's equations and a controlled differential inclusion. Conference Publications, 2013, 2013 (special) : 407-414. doi: 10.3934/proc.2013.2013.407 [8] Björn Birnir, Niklas Wellander. Homogenized Maxwell's equations; A model for ceramic varistors. Discrete & Continuous Dynamical Systems - B, 2006, 6 (2) : 257-272. doi: 10.3934/dcdsb.2006.6.257 [9] W. Wei, H. M. Yin. Global solvability for a singular nonlinear Maxwell's equations. Communications on Pure & Applied Analysis, 2005, 4 (2) : 431-444. doi: 10.3934/cpaa.2005.4.431 [10] Khalid Latrach, Hatem Megdiche. Time asymptotic behaviour for Rotenberg's model with Maxwell boundary conditions. Discrete & Continuous Dynamical Systems - A, 2011, 29 (1) : 305-321. doi: 10.3934/dcds.2011.29.305 [11] Armin Lechleiter, Marcel Rennoch. Non-linear Tikhonov regularization in Banach spaces for inverse scattering from anisotropic penetrable media. Inverse Problems & Imaging, 2017, 11 (1) : 151-176. doi: 10.3934/ipi.2017008 [12] Yonggeun Cho, Gyeongha Hwang, Tohru Ozawa. On small data scattering of Hartree equations with short-range interaction. Communications on Pure & Applied Analysis, 2016, 15 (5) : 1809-1823. doi: 10.3934/cpaa.2016016 [13] Giorgio Menegatti, Luca Rondi. Stability for the acoustic scattering problem for sound-hard scatterers. Inverse Problems & Imaging, 2013, 7 (4) : 1307-1329. doi: 10.3934/ipi.2013.7.1307 [14] Hermann Brunner, Chunhua Ou. On the asymptotic stability of Volterra functional equations with vanishing delays. Communications on Pure & Applied Analysis, 2015, 14 (2) : 397-406. doi: 10.3934/cpaa.2015.14.397 [15] M. Eller. On boundary regularity of solutions to Maxwell's equations with a homogeneous conservative boundary condition. Discrete & Continuous Dynamical Systems - S, 2009, 2 (3) : 473-481. doi: 10.3934/dcdss.2009.2.473 [16] Oleg Yu. Imanuvilov, Masahiro Yamamoto. Calderón problem for Maxwell's equations in cylindrical domain. Inverse Problems & Imaging, 2014, 8 (4) : 1117-1137. doi: 10.3934/ipi.2014.8.1117 [17] B. L. G. Jonsson. Wave splitting of Maxwell's equations with anisotropic heterogeneous constitutive relations. Inverse Problems & Imaging, 2009, 3 (3) : 405-452. doi: 10.3934/ipi.2009.3.405 [18] Cleverson R. da Luz, Gustavo Alberto Perla Menzala. Uniform stabilization of anisotropic Maxwell's equations with boundary dissipation. Discrete & Continuous Dynamical Systems - S, 2009, 2 (3) : 547-558. doi: 10.3934/dcdss.2009.2.547 [19] Andreas Kirsch. An integral equation approach and the interior transmission problem for Maxwell's equations. Inverse Problems & Imaging, 2007, 1 (1) : 159-179. doi: 10.3934/ipi.2007.1.159 [20] Yuri Kalinin, Volker Reitmann, Nayil Yumaguzin. Asymptotic behavior of Maxwell's equation in one-space dimension with thermal effect. Conference Publications, 2011, 2011 (Special) : 754-762. doi: 10.3934/proc.2011.2011.754

2016 Impact Factor: 1.094