A novel study on subspace migration for imaging of a sound-hard arc

Abstract In this study, the influence of a test vector selection used in subspace migration to reconstruct the shape of a sound-hard arc in a two-dimensional inverse acoustic problem is considered. In particular, a new mathematical structure of imaging function is constructed in terms of the Bessel functions of the order 0 , 1 , and 2 of the first kind based on the structure of singular vectors linked to the nonzero singular values of a Multi-Static Response (MSR) matrix. This structure indicates that imaging performance of subspace migration is highly related to the unknown shape of arc. The simulation results with noisy data indicate support for the derived structure.

[1]  Won-Kwang Park,et al.  Multi-frequency based location search algorithm of small electromagnetic inhomogeneities embedded in two-layered medium , 2012, Comput. Phys. Commun..

[2]  Rainer Kress,et al.  A hybrid method for sound-hard obstacle reconstruction , 2007 .

[3]  E. Iakovleva,et al.  Multistatic Response Matrix of a 3-D Inclusion in Half Space and MUSIC Imaging , 2007, IEEE Transactions on Antennas and Propagation.

[4]  Kuo Ming Lee,et al.  Inverse scattering via nonlinear integral equations for a Neumann crack , 2006 .

[5]  Eric Bonnetier,et al.  Enhanced Resolution in Structured Media , 2009, SIAM J. Appl. Math..

[6]  J. D. Shea,et al.  Three-dimensional microwave imaging of realistic numerical breast phantoms via a multiple-frequency inverse scattering technique. , 2010, Medical physics.

[7]  Dominique Lesselier,et al.  Electromagnetic MUSIC-type imaging of perfectly conducting, arc-like cracks at single frequency , 2009, J. Comput. Phys..

[8]  Mahta Moghaddam,et al.  Microwave Breast Imaging System Prototype with Integrated Numerical Characterization , 2012, Int. J. Biomed. Imaging.

[9]  Won-Kwang Park.  Detection of small electromagnetic inhomogeneities with inaccurate frequency , 2016 .

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

[11]  S. Siltanen,et al.  Inverse obstacle scattering with limited-aperture data , 2012 .

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

[13]  Won-Kwang Park.  On the imaging of thin dielectric inclusions buried within a half-space , 2010 .

[14]  Joseph Lipka,et al.  A Table of Integrals , 2010 .

[15]  Soon-Ik Jeon,et al.  A Prototype System for Early-Stage Breast Cancer Detection , 2015 .

[17]  L. Mönch.  On the numerical solution of the direct scattering problem for an open sound-hard arc , 1996 .

[18]  Won-Kwang Park,et al.  Analysis of subspace migrations in limited-view inverse scattering problems , 2013, Appl. Math. Lett..

[19]  Paul C. Beard,et al.  Photoacoustic tomography with a limited-aperture planar sensor and a reverberant cavity , 2007 .

[20]  Won-Kwang Park,et al.  Multi-frequency subspace migration for imaging of perfectly conducting, arc-like cracks in full- and limited-view inverse scattering problems , 2013, J. Comput. Phys..

[21]  Dominique Lesselier,et al.  MUSIC-type imaging of a thin penetrable inclusion from its multi-static response matrix , 2009 .

[22]  J. Kaipio,et al.  Approximation errors in nonstationary inverse problems , 2007 .

[23]  I. S. Gradshteyn,et al.  Table of Integrals, Series, and Products , 1976 .

[24]  Inverse Scattering from a Sound-Hard Crack via Two-Step Method , 2014 .

[25]  Dominique Lesselier,et al.  Fast electromagnetic imaging of thin inclusions in half-space affected by random scatterers , 2012 .

[26]  Lars Mönch,et al.  On the inverse acoustic scattering problem by an open arc: the sound-hard case , 1997 .

[27]  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..

[28]  Pedro Serranho,et al.  On the identification of the flatness of a sound-hard acoustic crack , 2004, Math. Comput. Simul..

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

[30]  Won-Kwang Park,et al.  Asymptotic properties of MUSIC-Type Imaging in Two-Dimensional Inverse Scattering from Thin Electromagnetic Inclusions , 2012, SIAM J. Appl. Math..

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

[32]  Some properties of subspace migrations in the limited-view inverse scattering problems , 2013 .