A multi-dimensional sampling method for locating small scatterers

A multiple signal classification (MUSIC)-like multi-dimensional sampling method (MDSM) is introduced to locate small three-dimensional scatterers using electromagnetic waves. The indicator is built with the most stable part of signal subspace of the multi-static response matrix on a set of combinatorial sampling nodes inside the domain of interest. It has two main advantages compared to the conventional MUSIC methods. First, the MDSM is more robust against noise. Second, it can work with a single incidence even for multi-scatterers. Numerical simulations are presented to show the good performance of the proposed method.

[1]  Hongkai Zhao,et al.  A direct imaging algorithm for extended targets , 2006 .

[2]  Ekaterina Iakovleva,et al.  A MUSIC Algorithm for Locating Small Inclusions Buried in a Half-Space from the Scattering Amplitude at a Fixed Frequency , 2005, Multiscale Model. Simul..

[3]  Josselin Garnier,et al.  A statistical approach to target detection and localization in the presence of noise , 2012 .

[4]  Xudong Chen,et al.  Imaging three-dimensional anisotropic scatterers in multilayered medium by multiple signal classification method with enhanced resolution. , 2012, Journal of the Optical Society of America. A, Optics, image science, and vision.

[5]  Ekaterina Iakovleva,et al.  MUSIC-Type Electromagnetic Imaging of a Collection of Small Three-Dimensional Inclusions , 2007, SIAM J. Sci. Comput..

[6]  Bangti Jin,et al.  A direct sampling method to an inverse medium scattering problem , 2012 .

[7]  Josselin Garnier,et al.  Stability and Resolution Analysis for a Topological Derivative Based Imaging Functional , 2012, SIAM J. Control. Optim..

[8]  A. Fannjiang,et al.  Compressive inverse scattering: I. High-frequency SIMO/MISO and MIMO measurements , 2009, 0906.5405.

[9]  J. Lovetri,et al.  Overview and Classification of Some Regularization Techniques for the Gauss-Newton Inversion Method Applied to Inverse Scattering Problems , 2009, IEEE Transactions on Antennas and Propagation.

[10]  Josselin Garnier,et al.  Detection, reconstruction, and characterization algorithms from noisy data in multistatic wave imaging , 2014 .

[11]  A.J. Devaney.  Time reversal imaging of obscured targets from multistatic data , 2005, IEEE Transactions on Antennas and Propagation.

[12]  A. Fannjiang,et al.  Compressive inverse scattering: II. Multi-shot SISO measurements with born scatterers , 2010 .

[13]  Xudong Chen,et al.  Twofold subspace-based optimization method for solving inverse scattering problems , 2009 .

[14]  Michael S. Zhdanov,et al.  3D electromagnetic inversion based on quasi-analytical approximation , 2000 .

[15]  Ekaterina Iakovleva,et al.  Direct Elastic Imaging of a Small Inclusion , 2008, SIAM J. Imaging Sci..

[16]  Xudong Chen,et al.  Multiple signal classification method for detecting point-like scatterers embedded in an inhomogeneous background medium. , 2010, The Journal of the Acoustical Society of America.

[17]  Qing Huo Liu,et al.  Through-wall imaging (TWI) by radar: 2-D tomographic results and analyses , 2005, IEEE Trans. Geosci. Remote. Sens..

[18]  Josselin Garnier,et al.  Imaging Schemes for Perfectly Conducting Cracks , 2011, SIAM J. Appl. Math..

[19]  Xudong Chen,et al.  MUSIC Imaging and Electromagnetic Inverse Scattering of Multiple-Scattering Small Anisotropic Spheres , 2007, IEEE Transactions on Antennas and Propagation.

[20]  Mathias Fink,et al.  Decomposition of the time reversal operator: Detection and selective focusing on two scatterers , 1996 .

[21]  Hanoch Lev-Ari,et al.  Intensity-only signal-subspace-based imaging. , 2007, Journal of the Optical Society of America. A, Optics, image science, and vision.

[22]  P. M. Berg,et al.  A finite-difference contrast source inversion method , 2008 .

[23]  D. Colton,et al.  The linear sampling method in inverse electromagnetic scattering theory , 2003 .

[24]  More on convexity and smoothness of operators , 2010 .

[25]  Thorkild B. Hansen,et al.  Inversion scheme for ground penetrating radar that takes into account the planar air-soil interface , 2000, IEEE Trans. Geosci. Remote. Sens..

[26]  Habib Ammari,et al.  Direct Reconstruction Methods in Ultrasound Imaging of Small Anomalies , 2012 .

[27]  Fred K. Gruber,et al.  Subspace-Based Localization and Inverse Scattering of Multiply Scattering Point Targets , 2007, EURASIP J. Adv. Signal Process..

[28]  Peter Monk,et al.  The Linear Sampling Method in Inverse Electromagnetic Scattering , 2010 .

[29]  Xudong Chen,et al.  MUSIC electromagnetic imaging with enhanced resolution for small inclusions , 2009 .

[30]  Rencheng Song,et al.  Imaging small three-dimensional elastic inclusions by an enhanced multiple signal classification method. , 2012, The Journal of the Acoustical Society of America.

[31]  Kimball A. Milton,et al.  Repulsive Casimir and Casimir–Polder forces , 2012, 1202.6415.

[32]  A. Kirsch.  The factorization method for Maxwell's equations , 2004 .