Fast identification of small perfectly conducting cracks without diagonal elements of multi-static response matrix

References

• Kress R. Inverse scattering from an open arc. Math Meth Appl Sci. 1995;18:267–293. doi: 10.1002/mma.1670180403
   Web of Science ®Google Scholar
• Chapko R, Kress R. A hybrid method for inverse boundary value problems in potential theory. J Inverse Ill-Posed Probl. 2005;13:27–40. doi: 10.1515/1569394053583711
   Google Scholar
• Kress R, Serranho P. A hybrid method for two-dimensional crack reconstruction. Inverse Probl. 2005;21:773–784. doi: 10.1088/0266-5611/21/2/020
   Web of Science ®Google Scholar
• Ivanyshyn O, Kress R. Inverse scattering for planar cracks via nonlinear integral equations. Math Meth Appl Sci. 2005;31:1221–1232. doi: 10.1002/mma.970
   Google Scholar
• Potthast R. On the convergence of a new newton-type method in inverse scattering. Inverse Probl. 2001;17:1419–1434. doi: 10.1088/0266-5611/17/5/312
   Web of Science ®Google Scholar
• Oliveri G, Salucci M, Anselmi N, et al. Compressive sensing as applied to inverse problems for imaging: theory, applications, current trends, and open challenges. IEEE Antennas Propag Mag. 2017;59:34–46. doi: 10.1109/MAP.2017.2731204
   Web of Science ®Google Scholar
• Caorsi S, Massa A, Pastorino M. A crack identification microwave procedure based on a genetic algorithm for nondestructive testing. IEEE Trans Antennas Propag. 2001;49:1812–1820. doi: 10.1109/8.982464
   Web of Science ®Google Scholar
• Salucci M, Anselmi N, Oliveri G, et al. Real-time NDT-NDE through an innovative adaptive partial least squares SVR inversion approach. IEEE Trans Geosci Remote Sens. 2016;54:6818–6832. doi: 10.1109/TGRS.2016.2591439
   Web of Science ®Google Scholar
• Álvarez D, Dorn O, Irishina N, et al. Crack reconstruction using a level-set strategy. J Comput Phys. 2009;228:5710–5721. doi: 10.1016/j.jcp.2009.04.038
   Web of Science ®Google Scholar
• Dorn O, Lesselier D. Level set methods for inverse scattering. Inverse Probl. 2006;22:R67–R131. doi: 10.1088/0266-5611/22/4/R01
   Web of Science ®Google Scholar
• Park WK, Lesselier D. MUSIC-type imaging of a thin penetrable inclusion from its far-field multi-static response matrix. Inverse Probl. 2009;25:075002.
   Web of Science ®Google Scholar
• Ventura G, Xu JX, Belytschko T. A vector level set method and new discontinuity approximations for crack growth by EFG. Int J Numer Meth Engng. 2002;54:923–944. doi: 10.1002/nme.471
   Web of Science ®Google Scholar
• Ammari H, Kang H, Lee H, et al. Asymptotic imaging of perfectly conducting cracks. SIAM J Sci Comput. 2010;32:894–922. doi: 10.1137/090749013
   Web of Science ®Google Scholar
• Joh YD, Kwon YM, Park WK. MUSIC-type imaging of perfectly conducting cracks in limited-view inverse scattering problems. Appl Math Comput. 2014;240:273–280.
   Web of Science ®Google Scholar
• Park WK, Lesselier D. Electromagnetic MUSIC-type imaging of perfectly conducting, arc-like cracks at single frequency. J Comput Phys. 2009;228:8093–8111. doi: 10.1016/j.jcp.2009.07.026
   Web of Science ®Google Scholar
• Bonnet M. Fast identification of cracks using higher-order topological sensitivity for 2-D potential problems. Eng Anal Bound Elem. 2011;35:223–235. doi: 10.1016/j.enganabound.2010.08.007
   Web of Science ®Google Scholar
• Bonnet M, Guzina B, Nemitz N. Fast non-iterative methods for defect identification. Rev Eur Mecan Num. 2008;17:571–582.
   Google Scholar
• Park WK. Performance analysis of multi-frequency topological derivative for reconstructing perfectly conducting cracks. J Comput Phys. 2017;335:865–884. doi: 10.1016/j.jcp.2017.02.007
   Web of Science ®Google Scholar
• Cakoni F, Colton D. The linear sampling method for cracks. Inverse Probl. 2003;19:279–295. doi: 10.1088/0266-5611/19/2/303
   Web of Science ®Google Scholar
• Colton D, Haddar H, Monk P. The linear sampling method for solving the electromagnetic inverse scattering problem. SIAM J Sci Comput. 2003;24(3):719–731. doi: 10.1137/S1064827501390467
   Web of Science ®Google Scholar
• Kirsch A, Ritter S. A linear sampling method for inverse scattering from an open arc. Inverse Probl. 2000;16(1):89–105. doi: 10.1088/0266-5611/16/1/308
   Web of Science ®Google Scholar
• Andrieux S, Abda AB. Identification of planar cracks by complete overdetermined data: inversion formulae. Inverse Probl. 1996;12:553–563. doi: 10.1088/0266-5611/12/5/002
   Web of Science ®Google Scholar
• Brühl M, Hanke M, Pidcock M. Crack detection using electrostatic measurements. Math Model Numer Anal. 2001;35:595–605. doi: 10.1051/m2an:2001128
   Web of Science ®Google Scholar
• Douvenot R, Lambert M, Lesselier D. Adaptive metamodels for crack characterization in eddy-current testing. IEEE Trans Magn. 2011;47:746–755. doi: 10.1109/TMAG.2011.2105883
   Web of Science ®Google Scholar
• Elcrat AR, Isakov V, Neculoiu O. On finding a surface crack from boundary measurements. Inverse Probl. 1995;11:343–351. doi: 10.1088/0266-5611/11/2/004
   Web of Science ®Google Scholar
• Ammari H, Garnier J, Kang H, et al. Imaging schemes for perfectly conducting cracks. SIAM J Appl Math. 2011;71(1):68–91. doi: 10.1137/100800130
   Web of Science ®Google Scholar
• Kwon YM, Park WK. Analysis of subspace migration in limited-view inverse scattering problems. Appl Math Lett. 2013;26:1107–1113. doi: 10.1016/j.aml.2013.05.015
   Web of Science ®Google Scholar
• Park WK. Improved subspace migration for imaging of small and arc-like perfectly conducting cracks. J Electromagn Waves Appl. 2014;28:410–419. doi: 10.1080/09205071.2013.866526
   Web of Science ®Google Scholar
• Park WK. Multi-frequency subspace migration for imaging of perfectly conducting, arc-like cracks in full- and limited-view inverse scattering problems. J Comput Phys. 2015;283:52–80. doi: 10.1016/j.jcp.2014.11.036
   Web of Science ®Google Scholar
• Nazarchuk ZT. Singular integral equations in diffraction theory. Lviv: Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences; 1994. (Mathematics and applications series).
   Google Scholar
• Ma YK, Park WK. Analysis of MUSIC-type imaging functionals for small two-dimensional electromagnetic inhomogeneities. J Electromagn Waves Appl. 2015;29:1430–1439. doi: 10.1080/09205071.2015.1047468
   Web of Science ®Google Scholar
• Mönch L. On the inverse acoustic scattering problem by an open arc: the sound-hard case. Inverse Probl. 1997;13:1379–1392. doi: 10.1088/0266-5611/13/5/017
   Web of Science ®Google Scholar
• Kim YJ, Jofre L, Flaviis FD, et al. Microwave reflection tomographic array for damage detection of civil structures. IEEE Trans Antennas Propag. 2003;51:3022–3032. doi: 10.1109/TAP.2003.818786
   Web of Science ®Google Scholar
• Park WK, Kim HP, Lee KJ, et al. MUSIC algorithm for location searching of dielectric anomalies from -parameters using microwave imaging. J Comput Phys. 2017;348:259–270. doi: 10.1016/j.jcp.2017.07.035
   Web of Science ®Google Scholar
• Park WK. Direct sampling method for anomaly imaging from scattering parameter. Appl Math Lett. 2018;81:63–71. doi: 10.1016/j.aml.2018.02.001
   Web of Science ®Google Scholar
• Seo T, Oh S, Jung D, et al. Noninvasive brain stimulation using a modulated microwave signal. J Electromagn Eng Sci. 2018;18(1):70–72. doi: 10.26866/jees.2018.18.1.70
   Web of Science ®Google Scholar
• Yang ST, Ling H. Application of compressive sensing to two-dimensional radar imaging using a frequency-scanned microstrip leaky wave antenna. J Electromagn Eng Sci. 2017;17(3):113–119. doi: 10.5515/JKIEES.2017.17.3.113
   Web of Science ®Google Scholar