`a`
Inverse Problems and Imaging (IPI)
 

The generalized linear sampling and factorization methods only depends on the sign of contrast on the boundary
Pages: 1107 - 1119, Issue 6, December 2017

doi:10.3934/ipi.2017051      Abstract        References        Full text (495.0K)           Related Articles

Lorenzo Audibert - EDF R&D, Departement STEP, 6 quai Watier, 78401, Chatou CEDEX, France (email)

1 L. Audibert, A. Girard and H. Haddar, Identifying defects in an unknown background using differential measurements, Inverse Problems and Imaging, 9 (2015), 625-643.       
2 L. Audibert and H. Haddar, A generalized formulation of the linear sampling method with exact characterization of targets in terms of farfield measurements, Inverse Problems, 30 (2014), 035011, 20pp.       
3 L. Audibert and H. Haddar, The generalized linear sampling method for limited aperture measurements, SIAM J. Imaging Sci., 10 (2017), 845-870.       
4 A.-S. Bonnet-Ben Dhia, L. Chesnel and H. Haddar, On the use of $T$-coercivity to study the interior transmission eigenvalue problem, C. R. Math. Acad. Sci. Paris, 349 (2011), 647-651.       
5 F. Cakoni and D. Colton, Qualitative Methods in Inverse Scattering Theory, Interaction of Mechanics and Mathematics. Springer-Verlag, Berlin, 2006. An introduction.       
6 F. Cakoni, D. Colton and H. Haddar, Inverse Scattering Theory and Transmission Eigenvalues, volume 88 of CBMS Series, SIAM publications, 2016.       
7 F. Cakoni and I. Harris, The factorization method for a defective region in an anisotropic material, Inverse Problems, 31 (2015), 025002, 22pp.       
8 H. Haddar, F. Cakoni and S. Meng, Boundary integral equations for the transmission eigenvalue problem for aaxwell equations, J. Integral Equations Appl., 27 (2015), 375-406.       
9 A. Cossonnière and H. Haddar, Surface integral formulation of the interior transmission problem, J. Integral Equations Appl., 25 (2013), 341-376.       
10 L. Evgeny and L. Armin, Monotonicity in inverse medium scattering.
11 B. Gebauer, The factorization method for real elliptic problems, Zeitschrift für Analysis und ihre Anwendungen, 25 (2006), 81-102.       
12 D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Classics in Mathematics. Springer-Verlag, Berlin, 2001. Reprint of the 1998 edition.       
13 P. Grisvard, Elliptic Problems in Nonsmooth Domains, volume 24 of Monographs and Studies in Mathematics, Pitman (Advanced Publishing Program), Boston, MA, 1985.       
14 A. Kirsch, The factorization method for a class of inverse elliptic problems, Mathematische Nachrichten, 278 (2005), 258-277.       
15 A. Kirsch, A note on Sylvester's proof of discreteness of interior transmission eigenvalues, Comptes Rendus Mathématique, 354 (2016), 377-382.       
16 A. Kirsch and N. Grinberg, The Factorization Method for Inverse Problems, volume 36 of Oxford Lecture Series in Mathematics and its Applications, Oxford University Press, Oxford, 2008.       
17 J. Sylvester, Discreteness of transmission eigenvalues via upper triangular compact operators, SIAM J. Math. Anal., 44 (2012), 341-354.       
18 J. Yang, B. Zhang and H. Zhang, The factorization method for reconstructing a penetrable obstacle with unknown buried objects, SIAM Journal of Applied Mathematics, 73 (2013), 617-635.       

Go to top