L. Bourgeois, F. Le-louer, and E. Lunéville, On the use of Lamb modes in the linear sampling method for elastic waveguides, Inverse Problems, vol.27, issue.5, pp.266-5611
DOI : 10.1088/0266-5611/27/5/055001
URL : https://hal.archives-ouvertes.fr/hal-00849575

L. Bourgeois and E. Lunéville, On the use of the linear sampling method to identify cracks in elastic waveguides, 2013) 025017. URL http://stacks.iop.org, pp.266-5611, 25017.
DOI : 10.1088/0266-5611/29/2/025017
URL : https://hal.archives-ouvertes.fr/hal-00937686

P. Huthwaite, Evaluation of inversion approaches for guided wave 840 thickness mapping, Proceedings of the Royal Society of London A: Mathematical , Physical and Engineering Sciences, vol.470470, issue.845, p.20140063, 2166.
DOI : 10.1098/rspa.2014.0063
URL : http://rspa.royalsocietypublishing.org/content/royprsa/470/2166/20140063.full.pdf

A. Demma, P. Cawley, M. Lowe, A. Roosenbrand, and B. Pavlakovic, The reflection of guided waves from notches in pipes: a guide for interpreting corrosion measurements, NDT & E International, vol.37, issue.3, 2004.
DOI : 10.1016/j.ndteint.2003.09.004

S. Fletcher, M. J. Lowe, M. Ratassepp, and C. Brett, Detection of Axial Cracks in Pipes Using Focused Guided Waves, Journal of Nondestructive Evaluation, vol.210, issue.4
DOI : 10.1243/PIME_PROC_1996_210_415_02

C. Willey, F. Simonetti, P. Nagy, and G. Instanes, Guided wave tomography of pipes with high-order helical modes, NDT & E International, vol.65, issue.860, p.0963869514000449, 2014.
DOI : 10.1016/j.ndteint.2014.03.010

J. Rao, M. Ratassepp, Z. S. Fan, M. Rodriguez, M. Deschamps et al., Guided Wave Tomography Based on Full Waveform Inversion, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol.63, issue.5, pp.737-745, 2005.
DOI : 10.1109/TUFFC.2016.2536144

L. L. Jeune, S. Robert, E. L. Villaverde, and C. Prada, Plane Wave Imaging for ultrasonic non-destructive testing: Generalization to multimodal imaging, Ultrasonics, vol.64
DOI : 10.1016/j.ultras.2015.08.008
URL : https://hal.archives-ouvertes.fr/hal-01322017

D. Colton and A. Kirsch, A simple method for solving inverse scattering problems in the resonance region, Inverse Problems, vol.12, issue.4, pp.383-393, 1996.
DOI : 10.1088/0266-5611/12/4/003

T. Arens, Linear sampling methods for 2D inverse elastic wave scattering, Inverse Problems, vol.17, issue.5, p.885
DOI : 10.1088/0266-5611/17/5/314

, Inverse Problems, vol.17175, issue.5, pp.1445-14640266, 2001.

A. Charalambopoulos, D. Gintides, and K. Kiriaki, The linear sampling method for non-absorbing penetrable elastic bodies, Inverse Problems, vol.19, issue.3, p.890, 2003.
DOI : 10.1088/0266-5611/19/3/305

D. Colton, H. Haddar, and P. Monk, The Linear Sampling Method for Solving the Electromagnetic Inverse Scattering Problem, SIAM Journal on Scientific Computing, vol.24, issue.3, pp.719-731, 2002.
DOI : 10.1137/S1064827501390467
URL : https://hal.archives-ouvertes.fr/hal-00744171

H. Haddar and P. Monk, The linear sampling method for solving the electromagnetic inverse medium problem, Inverse Problems, vol.18, issue.3, pp.891-9060266, 2002.
DOI : 10.1088/0266-5611/18/3/323
URL : https://hal.archives-ouvertes.fr/hal-00744180

]. Y. Xu, C. Mawata, and W. Lin, Generalized dual space indicator method for underwater imaging, Inverse Problems, vol.16, issue.6, pp.900-1761, 2000.
DOI : 10.1088/0266-5611/16/6/311

A. Charalambopoulos, D. Gintides, K. Kiriaki, and A. Kirsch, THE FACTORIZATION METHOD FOR AN ACOUSTIC WAVE GUIDE, Mathematical Methods in Scattering Theory and Biomedical Engineering, pp.120-127, 2006.
DOI : 10.1142/9789812773197_0013

L. Bourgeois and E. Lunéville, The linear sampling method in a waveguide: a modal formulation, Inverse Problems, vol.24, issue.1, pp.266-5611, 2008.
DOI : 10.1088/0266-5611/24/1/015018
URL : https://hal.archives-ouvertes.fr/hal-00876221

]. P. Monk and V. Selgas, Sampling type methods for an inverse waveguide problem, Inverse Problems and Imaging, vol.6, issue.4, pp.910-709, 2012.
DOI : 10.3934/ipi.2012.6.709

L. Borcea and D. Nguyen, Imaging with electromagnetic waves in terminating waveguides, Inverse Problems and Imaging, vol.10, issue.4
DOI : 10.3934/ipi.2016027

F. Cakoni and D. Colton, The linear sampling method for cracks, Inverse Problems, vol.19, issue.2, pp.279-2950266, 2003.
DOI : 10.1088/0266-5611/19/2/303

F. Ben-hassen, Y. Boukari, and H. Haddar, Application of the linear sampling 920 method to identify cracks with impedance boundary conditions, Inverse Probl. Sci. Eng, vol.21, issue.2

F. Pourahmadian, B. B. Guzina, and H. Haddar, Generalized linear sampling 925 method for elastic-wave sensing of heterogeneous fractures, Inverse Problems, vol.335, issue.5, p.55007
DOI : 10.1088/1361-6420/33/5/055007
URL : http://arxiv.org/pdf/1605.08743

Q. Chen, H. Haddar, A. Lechleiter, and P. Monk, A sampling method for inverse scattering in the time domain, Inverse Problems, vol.26, issue.8, pp.266-5611085001
DOI : 10.1088/0266-5611/26/8/085001
URL : https://hal.archives-ouvertes.fr/hal-00739329

P. Monk, V. Selgas, V. Baronian, L. Bourgeois, and A. Recoquillay, An inverse acoustic waveguide problem in the time domain Imaging an acoustic waveguide from surface data in the time domain, 2016) 055001. URL http://stacks.iop.org, pp.266-5611, 2016.

L. Bourgeois and S. Fliss, On the identification of defects in a periodic waveg- 940 uide from far field data, Inverse Problems, vol.30309, issue.9, pp.266-5611

H. Brezis, Functional analysis, Sobolev spaces and partial differential equations, 2011.
DOI : 10.1007/978-0-387-70914-7

A. Recoquillay, Méthodes d'´ echantillonnage appliquéesappliquéesà l'imagerie de 945

V. Baronian, A. S. Bonnet-ben-dhia, and E. Lunéville, Transparent boundary conditions for the harmonic diffraction problem in an elastic waveguide, Journal of Computational and Applied Mathematics, vol.234, issue.6, 1945.
DOI : 10.1016/j.cam.2009.08.045
URL : https://hal.archives-ouvertes.fr/hal-00975075

W. B. Fraser, Orthogonality relation for the Rayleigh???Lamb modes of vibration of a plate, The Journal of the Acoustical Society of America, vol.59, issue.1, pp.215-216, 1976.
DOI : 10.1121/1.380851

V. Pagneux and A. , Lamb wave propagation in elastic waveguides with variable thickness, Proc. R. Soc. Lond. Ser. A Math, pp.1315-13391612, 2005.
DOI : 10.1098/rspa.2005.1612

V. Baronian, Couplage des méthodes modale etélémentsetéléments finis pour la diffraction des ondesélastiquesondesélastiques guidées, Ecole Polytechnique, p.960, 2009.

L. Bourgeois and E. Lunéville, The linear sampling method in a waveguide: A formulation based on modes, Journal of Physics: Conference Series, vol.135, p.12023, 2008.
DOI : 10.1088/1742-6596/135/1/012023
URL : https://hal.archives-ouvertes.fr/hal-00873074

D. Colton, M. Piana, and R. Potthast, A simple method using Morozov's discrepancy principle for solving inverse scattering problems, Inverse Problems, vol.13, issue.6, pp.1477-1493, 1997.
DOI : 10.1088/0266-5611/13/6/005

A. Moitra, Super-resolution, Extremal Functions and the Condition Number of Vandermonde Matrices, Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing, STOC '15, pp.821-830
DOI : 10.1090/S0273-0979-1985-15349-2
URL : http://arxiv.org/pdf/1408.1681

A. Imperiale, S. Chatillon, P. Calmon, N. Leymarie, S. Imperiale et al., UT Simulation of Embedded Parametric Defects Using a Hybrid Model Based Upon Spectral Finite Element and Domain Decomposition Methods, Proceedings of the 19th World Conference on Non- Destructive Testing. 975 [38] K. Jezzine, Approche modale pour la simulation globale des contrôles nondestructifs par ondesélastiquesondesélastiques guidées, 2006.

D. Royer and E. Dieulesaint, OndesélastiquesOndesélastiques dans les solides, Interaction of Mechanics and Mathematics, vol.1, 1996.