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Applicable Analysis
An International Journal
Volume 76, 2000 - Issue 3-4
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Original Articles

New characterizations of solutions in inverse scattering theory

Andreas Kirsch Mathematisches Institut II, Universität Karlsruhe, Karlsruhe, TH, D-76128, Germany
Pages 319-350 | Received 01 May 2000, Published online: 10 May 2007

Citations (38)

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Read on this site (3)

Meiman Sun & Guozheng Yan. (2021) The direct and inverse scattering problems for penetrable and impenetrable mixed obstacles. Applicable Analysis 100:11, pages 2315-2333.
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Yann Grisel, Jèrèmie Fourbil & Vincent Mouysset. (2016) An optimization approach for the localization of defects in an inhomogeneous medium from acoustic far-field measurements at a fixed frequency. Inverse Problems in Science and Engineering 24:7, pages 1162-1185.
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Masaru Ikehata. (2007) Extracting discontinuity in a heat conductive body. One-space dimensional case. Applicable Analysis 86:8, pages 963-1005.
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Articles from other publishers (35)

Roland Griesmaier, Marvin Knöller & Rainer Mandel. (2022) Inverse medium scattering for a nonlinear Helmholtz equation. Journal of Mathematical Analysis and Applications 515:1, pages 126356.
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Pinchao Meng, Xinyu Wang & Weishi Yin. (2022) ODE-RU: a dynamical system view on recurrent neural networks. Electronic Research Archive 30:1, pages 257-271.
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Jianli Xiang & Guozheng Yan. (2021) The factorization method for inhomogeneous medium with an impenetrable obstacle. Computational and Applied Mathematics 40:8.
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Fioralba Cakoni, Houssem Haddar & Armin Lechleiter. (2019) On the Factorization Method for a Far Field Inverse Scattering Problem in the Time Domain. SIAM Journal on Mathematical Analysis 51:2, pages 854-872.
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E. I. Shifrin. (2017) Factorization method in the geometric inverse problem of static elasticity. Mechanics of Solids 51:5, pages 562-570.
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Armin Lechleiter. 2015. Encyclopedia of Applied and Computational Mathematics. Encyclopedia of Applied and Computational Mathematics 479 485 .
Martin Hanke-Bourgeois & Andreas Kirsch. 2015. Handbook of Mathematical Methods in Imaging. Handbook of Mathematical Methods in Imaging 591 647 .
Martin Hanke-Bourgeois & Andreas Kirsch. 2020. Handbook of Mathematical Methods in Imaging. Handbook of Mathematical Methods in Imaging 1 51 .
Konstantinos A Anagnostopoulos, Antonios Charalambopoulos & Andreas Kleefeld. (2013) The factorization method for the acoustic transmission problem. Inverse Problems 29:11, pages 115015.
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Bastian Harrach & Marcel Ullrich. (2013) Monotonicity-Based Shape Reconstruction in Electrical Impedance Tomography. SIAM Journal on Mathematical Analysis 45:6, pages 3382-3403.
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Masaru Ikehata, Esa Niemi & Samuli Siltanen. (2012) Inverse obstacle scattering with limited-aperture data. Inverse Problems & Imaging 6:1, pages 77-94.
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Armin Lechleiter. (2011) Explicit characterization of the support of non-linear inclusions. Inverse Problems & Imaging 5:3, pages 675-694.
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Martin Hanke & Andreas Kirsch. 2011. Handbook of Mathematical Methods in Imaging. Handbook of Mathematical Methods in Imaging 501 550 .
Masaru Ikehata. (2010) Mittag–Leffler's function, Vekua transform and an inverse obstacle scattering problem. Inverse Problems 26:4, pages 045004.
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Jijun Liu & Haibing Wang. 2011. Optimization and Regularization for Computational Inverse Problems and Applications. Optimization and Regularization for Computational Inverse Problems and Applications 205 247 .
Adrian I. Nachman, Lassi Päivärinta & Ari Teirilä. (2007) On imaging obstacles inside inhomogeneous media. Journal of Functional Analysis 252:2, pages 490-516.
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Rainer Kress. (2007) Uniqueness and numerical methods in inverse obstacle scattering. Journal of Physics: Conference Series 73, pages 012003.
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Antonios Charalambopoulos, Andreas Kirsch, Konstantinos A Anagnostopoulos, Drossos Gintides & Kiriakie Kiriaki. (2007) The factorization method in inverse elastic scattering from penetrable bodies. Inverse Problems 23:1, pages 27-51.
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David Colton & Rainer Kress. (2006) Using fundamental solutions in inverse scattering. Inverse Problems 22:3, pages R49-R66.
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Roland Potthast. (2006) A survey on sampling and probe methods for inverse problems. Inverse Problems 22:2, pages R1-R47.
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Konstantinos A Anagnostopoulos & Antonios Charalambopoulos. (2006) The linear sampling method for the transmission problem in 2D anisotropic elasticity. Inverse Problems 22:2, pages 553-577.
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T. Arens & N. Grinberg. (2004) A Complete Factorization Method for Scattering by Periodic Surfaces. Computing 75:2-3, pages 111-132.
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Andreas Kirsch. (2005) The factorization method for a class of inverse elliptic problems. Mathematische Nachrichten 278:3, pages 258-277.
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Andreas Kirsch. (2004) The factorization method for Maxwell's equations. Inverse Problems 20:6, pages S117-S134.
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N.I Grinberg & A Kirsch. (2004) The factorization method for obstacles with a-priori separated sound-soft and sound-hard parts. Mathematics and Computers in Simulation 66:4-5, pages 267-279.
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Tilo Arens. (2004) Why linear sampling works. Inverse Problems 20:1, pages 163-173.
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David Colton, Houssem Haddar & Michele Piana. (2003) The linear sampling method in inverse electromagnetic scattering theory. Inverse Problems 19:6, pages S105-S137.
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Tilo Arens & Andreas Kirsch. (2003) The factorization method in inverse scattering from periodic structures. Inverse Problems 19:5, pages 1195-1211.
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Tony F. Chan & Xue-Cheng Tai. (2003) Identification of Discontinuous Coefficients in Elliptic Problems Using Total Variation Regularization. SIAM Journal on Scientific Computing 25:3, pages 881-904.
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Andreas Kirsch. 2003. Topics in Computational Wave Propagation. Topics in Computational Wave Propagation 337 365 .
N I Grinberg. (2002) Obstacle visualization via the factorization method for the mixed boundary value problem. Inverse Problems 18:6, pages 1687-1704.
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Andreas Kirsch. (2002) The MUSIC-algorithm and the factorization method in inverse scattering theory for inhomogeneous media. Inverse Problems 18:4, pages 1025-1040.
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Michael Brandfass, Aaron D Lanterman & Karl F Warnick. (2001) A comparison of the Colton–Kirsch inverse scattering methods with linearized tomographic inverse scattering. Inverse Problems 17:6, pages 1797-1816.
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T Arens. (2001) Linear sampling methods for 2D inverse elastic wave scattering. Inverse Problems 17:5, pages 1445-1464.
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N I Grinberg. (2001) Obstacle localization in an homogeneous half-space. Inverse Problems 17:4, pages 1113-1125.
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