An extended direct factorization method for inverse scattering with limited aperture data

References

• Colton D, Coyle J, Monk P. Recent developments in inverse acoustic scattering theory. SIAM Rev. 2000;42:369–414. doi: 10.1137/S0036144500367337
   Web of Science ®Google Scholar
• Colton D, Kress R. Inverse acoustic and electromagnetic scattering theory. New York: Springer; 2012.
   Google Scholar
• Ammari H, Chow YT, Zou J. Phased and phaseless domain reconstructions in the inverse scattering problem via scattering coefficients. SIAM J Appl Math. 2016;76:1000–1030. doi: 10.1137/15M1043959
   Web of Science ®Google Scholar
• Cakoni F, Rezac JD. Direct imaging of small scatterers using reduced time dependent data. J Comput Phys. 2017;338:371–387. doi: 10.1016/j.jcp.2017.02.061
   Web of Science ®Google Scholar
• Fotopoulos G, Harju M. Inverse scattering with fixed observation angle data in 2D. Inverse Problems Sci Eng. 2016;25:1492–1507. doi: 10.1080/17415977.2016.1267170
   Web of Science ®Google Scholar
• Guo Y, Hmberg D, Hu G, et al. A time domain sampling method for inverse acoustic scattering problems. J Comput Phys. 2016;314:647–660. doi: 10.1016/j.jcp.2016.03.046
   Web of Science ®Google Scholar
• Li J, Liu H, Wang Q. Enhanced multilevel linear sampling methods for inverse scattering problems. J Comput Phys. 2014;257:554–571. doi: 10.1016/j.jcp.2013.09.048
   Web of Science ®Google Scholar
• Liu K, Xu Y, Zou J. A parallel radial bisection algorithm for inverse scattering problems. Inverse Prob Sci Eng. 2013;21:197–209. doi: 10.1080/17415977.2012.686498
   Web of Science ®Google Scholar
• Liu X. A novel sampling method for multiple multiscale targets from scattering amplitudes at a fixed frequency. Inverse Prob. 2017;33:085011.
   Web of Science ®Google Scholar
• Liu X, Zhang B. Recent progress on the factorization method for inverse acoustic scattering problems. SCIENTIA SINICA Math. 2015;45:873–890.
   Google Scholar
• Giorgi G, Brignone M, Aramini R, et al. Application of the inhomogeneous Lippmann–Schwinger equation to inverse scattering problems. SIAM J Appl Math. 2013;73:212–231. doi: 10.1137/120869584
   Web of Science ®Google Scholar
• Murch RD, Tan DGH, Wall DJN. Newton-Kantorovich method applied to two-dimensional inverse scattering for an exterior Helmholtz problem. Inverse Prob. 1988;4:1117–1128. doi: 10.1088/0266-5611/4/4/012
   Web of Science ®Google Scholar
• Roger A. Newton-kantorovitch algorithm applied to an electromagnetic inverse problem. IEEE Trans Antennas Propagat. 1981;29:232–238. doi: 10.1109/TAP.1981.1142588
   Web of Science ®Google Scholar
• Arens T, Lechleiter A. The linear sampling method revisited. J Integral Equ Appl. 2009;21:179–202. doi: 10.1216/JIE-2009-21-2-179
   Web of Science ®Google Scholar
• Cakoni F, Colton D. A qualitative approach to inverse scattering theory. New York: Springer; 2013.
   Google Scholar
• Colton D, Haddar H, Piana M. The linear sampling method in inverse electromagnetic scattering theory. Inverse Prob. 2003;19:S105–S137. doi: 10.1088/0266-5611/19/6/057
   Web of Science ®Google Scholar
• Potthast R. A survey on sampling and probe methods for inverse problems. Inverse Prob. 2006;22:R1–R47. doi: 10.1088/0266-5611/22/2/R01
   Web of Science ®Google Scholar
• Cakoni F, Colton D, Monk P. The linear sampling method in inverse electromagnetic scattering. Philadelphia (PA): SIAM; 2011.
   Google Scholar
• Kirsch A, Grinberg N. The factorization method for inverse problems. Oxford: OUP; 2008.
   Google Scholar
• Ito K, Jin B, Zou J. A direct sampling method to an inverse medium scattering problem. Inverse Prob. 2012;28:025003. doi: 10.1088/0266-5611/28/2/025003
   Web of Science ®Google Scholar
• Bellis C, Bonnet M, Cakoni F. Acoustic inverse scattering using topological derivative of far-field measurements-basedL2cost functionals. Inverse Prob. 2013;29:075012. doi: 10.1088/0266-5611/29/7/075012
   Web of Science ®Google Scholar
• Bonnet M, Cakoni F. Analysis of topological derivative as a tool for qualitative identification. Inverse Problems. 2019.
   Google Scholar
• Lour FL, Rapún M-L. Topological sensitivity for solving inverse multiple scattering problems in three-dimensional electromagnetism. part i: One step method. SIAM J Imag Sci. 2017;10:1291–1321. doi: 10.1137/17M1113850
   Web of Science ®Google Scholar
• Lour FL, Rapún M-L. Topological sensitivity for solving inverse multiple scattering problems in three-dimensional electromagnetism. part II: Iterative method. SIAM J Imag Sci. 2018;11:734–769. doi: 10.1137/17M1148359
   Web of Science ®Google Scholar
• Yuan H, Bracq G, Lin Q. Inverse acoustic scattering by solid obstacles: topological sensitivity and its preliminary application. Inverse Problems Sci Eng. 2015;24:92–126. doi: 10.1080/17415977.2015.1017483
   Web of Science ®Google Scholar
• Leem KH, Liu J, Pelekanos G. Two direct factorization methods for inverse scattering problems. Inverse Prob. 2018;34:125004.
   Web of Science ®Google Scholar
• Leem KH, Liu J, Pelekanos G. An adaptive quadrature-based factorization method for inverse acoustic scattering problems. Inverse Problems Sci Engin. 2019;27(3):299–316. doi: 10.1080/17415977.2018.1459600
   Web of Science ®Google Scholar
• Bao G, Liu J. Numerical solution of inverse scattering problems with multi-experimental limited aperture data. SIAM J Sci Comput. 2003;25:1102–1117. doi: 10.1137/S1064827502409705
   Web of Science ®Google Scholar
• Barucq H, Bekkey C, Djellouli R. A multi-step procedure for enriching limited two-dimensional acoustic far-field pattern measurements. J Inverse Ill-posed Prob. 2010;18.
   Web of Science ®Google Scholar
• Barucq H, Bekkey C, Djellouli R. Full aperture reconstruction of the acoustic far-field pattern from few measurements. Commun Comput Phys. 2012;11:647–659. doi: 10.4208/cicp.281209.150610s
   Web of Science ®Google Scholar
• Djellouli R, Tezaur R, Farhat C. On the solution of inverse obstacle acoustic scattering problems with a limited aperture. Mathematical and Numerical Aspects of Wave Propagation WAVES 2003, Springer Berlin Heidelberg, 2003, pp. 625–630.
   Google Scholar
• Ochs Jr RL. The limited aperture problem of inverse acoustic scattering: Dirichlet boundary conditions. SIAM J Appl Math. 1987;47:1320–1341. doi: 10.1137/0147087
   Web of Science ®Google Scholar
• You Y-X, Miao G-P, Liu Y-Z. A numerical method for solving the limited aperture problem in three-dimensional inverse obstacle scattering. Int J Nonlinear Sci Numer Simul. 2001;2. doi: 10.1515/IJNSNS.2001.2.1.29
   Web of Science ®Google Scholar
• Zinn A. On an optimisation method for the full- and the limited-aperture problem in inverse acoustic scattering for a sound-soft obstacle. Inverse Prob. 1989;5:239–253. doi: 10.1088/0266-5611/5/2/009
   Web of Science ®Google Scholar
• Ikehata M, Niemi E, Siltanen S. Inverse obstacle scattering with limited-aperture data. Inverse Prob Imag. 2012;6:77–94. doi: 10.3934/ipi.2012.6.77
   Web of Science ®Google Scholar
• Audibert L, Haddar H. A generalized formulation of the linear sampling method with exact characterization of targets in terms of farfield measurements. Inverse Prob. 2014;30:035011. doi: 10.1088/0266-5611/30/3/035011
   Web of Science ®Google Scholar
• Audibert L, Haddar H. The generalized linear sampling method for limited aperture measurements. SIAM J Imag Sci. 2017;10:845–870. doi: 10.1137/16M110112X
   Web of Science ®Google Scholar
• Liu X, Sun J. Data recovery in inverse scattering: from limited-aperture to full-aperture. J Comput Phys. 2019;386:350–364. doi: 10.1016/j.jcp.2018.10.036
   Web of Science ®Google Scholar
• Liu J, Sun J. Extended sampling method in inverse scattering. Inverse Prob. 2018;34:085007. doi: 10.1088/1361-6420/aaca90
   Web of Science ®Google Scholar
• Potthast R, Sylvester J, Kusiak S. A range test for determining scatterers with unknown physical properties. Inverse Prob. 2003;19:533–547. doi: 10.1088/0266-5611/19/3/304
   Web of Science ®Google Scholar
• Aramini R, Brignone M, Piana M. The linear sampling method without sampling. Inverse Prob. 2006;22:2237–2254. doi: 10.1088/0266-5611/22/6/020
   Web of Science ®Google Scholar
• Benning M, Burger M. Modern regularization methods for inverse problems. Acta Numer. 2018;27:1–111. doi: 10.1017/S0962492918000016
   Web of Science ®Google Scholar
• Brignone M, Bozza G, Aramini R, et al. A fully no-sampling formulation of the linear sampling method for three-dimensional inverse electromagnetic scattering problems. Inverse Prob. 2008;25:015014.
   Web of Science ®Google Scholar
• Harris I, Kleefeld A. Analysis of new direct sampling indicators for far-field measurements. Inverse Prob. 2019;35:054002. doi: 10.1088/1361-6420/ab08be
   Web of Science ®Google Scholar
• Liu H, Zou J. Zeros of the bessel and spherical bessel functions and their applications for uniqueness in inverse acoustic obstacle scattering. IMA J Appl Math. 2007;72:817–831. doi: 10.1093/imamat/hxm013
   Web of Science ®Google Scholar
• Ben-Israel A, Charnes A. Contributions to the theory of generalized inverses. J Soc Ind Appl Math. 1963;11:667–699. doi: 10.1137/0111051
   Google Scholar
• Climent J-J, Thome N, Wei Y. A geometrical approach on generalized inverses by neumann-type series. Linear Algebra Appl. 2001;332–334:533–540. doi: 10.1016/S0024-3795(01)00309-3
   Web of Science ®Google Scholar
• Tanabe K. Neumann-type expansion of reflexive generalized inverses of a matrix and the hyperpower iterative method. Linear Algebra Appl. 1975;10:163–175. doi: 10.1016/0024-3795(75)90008-7
   Web of Science ®Google Scholar
• Atherton T, Kerbyson D. Size invariant circle detection. Image Vision Comput. 1999;17:795–803. doi: 10.1016/S0262-8856(98)00160-7
   Web of Science ®Google Scholar
• Li Z, Deng Z, Sun J. Limited aperture inverse scattering problems using Bayesian approach and extended sampling method. arXiv e-prints, (2019), p. arXiv:1905.12222.
   Google Scholar