J. D. Achenbach, Quantitative nondestructive evaluation, International Journal of Solids and Structures, vol.37, issue.1-2, pp.13-27, 1980.
DOI : 10.1016/S0020-7683(99)00074-8

D. N. Alleyne, The nondestructive testing of plates using ultrasonic Lamb waves, 1991.

H. T. Banks and K. L. Bihari, Modelling and estimating uncertainty in parameter estimation , Inverse Probs, pp.95-102, 2001.

H. T. Banks and K. Kunisch, Estimation Techniques for Distributed Parameter Systems, 1989.
DOI : 10.1007/978-1-4612-3700-6

J. L. Buchanan, R. P. Gilbert, and M. Y. Ou, Recovery of the parameters of cancellous bone by inversion of effective velocities, and transmission and reflection coefficients, Inverse Problems, vol.27, issue.12, p.125006, 2011.
DOI : 10.1088/0266-5611/27/12/125006

D. Byatt, I. Coope, and C. Price, 40 Years of the Nelder-Mead algorithm, Talk, 2003.

D. Cao, W. B. Beydoun, S. C. Singh, and A. Tarantola, A simultaneous inversion for background velocity and impedance maps, Geophys, pp.458-469, 1990.

X. Chen, T. M. Grzegorczyk, B. Wu, . J. Pacheco-jr, and J. A. Kong, Robust method to retrieve the constitutive effective parameters of metamaterials, Physical Review E, vol.70, issue.1, p.16608, 2004.
DOI : 10.1103/PhysRevE.70.016608

J. F. Devlin, A Simple and Powerful Method of Parameter Estimation Using Simplex Optimization, Ground Water, vol.4, issue.2, pp.323-327, 1994.
DOI : 10.1111/j.1745-6584.1994.tb00647.x

H. L. Cox, Estimation of macro velocity models by wave field extrapolation, 1991.

A. Dubois, J. Geffrin, and K. Belkebir, Imaging of dielectric cylinders from experimental stepped-frequency data, Applied Physics Letters, vol.88, issue.16, p.164104, 2006.
DOI : 10.1063/1.2196067

URL : https://hal.archives-ouvertes.fr/hal-00083976

C. Gelis, J. Virieux, and G. Grandjean, Two-dimensional elastic full waveform inversion using Born and Rytov formulations in the frequency domain, Geophysical Journal International, vol.168, issue.2, pp.605-633, 2007.
DOI : 10.1111/j.1365-246X.2006.03135.x

URL : https://hal.archives-ouvertes.fr/hal-00758745

R. Guillermin, Caractérisation d'objets enfouis dans des sédiments marins par imagerie acoustique, 2000.

P. Huthwaite and F. Simonetti, High-resolution imaging without iteration: a fast and robust method for breast ultrasound tomography, The Journal of the Acoustical Society of America, vol.130, issue.3, pp.1721-1734, 2011.
DOI : 10.1121/1.3613936

V. Isakov, Inverse obstacle problems, Inverse Probs, p.123002, 2009.

M. L. Johnson, M. Lindsay, and L. M. Faunt, [1] Parameter estimation by least-squares methods, Numerical Computer Methods Academic, 1992.
DOI : 10.1016/0076-6879(92)10003-V

D. Kurrant and E. Fear, Regional estimation of the dielectric properties of inhomogeneous objects using near-field reflection data, Inverse Probs, p.75001, 2012.

J. Lagarias, J. Reeds, M. Wright, and P. Wright, Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions, SIAM Journal on Optimization, vol.9, issue.1, pp.112-147, 1998.
DOI : 10.1137/S1052623496303470

L. Montero and R. J. , New developments on quantitative imaging using ultrasonic waves, 2009.

G. Lefeuve-mesgouez, A. Mesgouez, E. Ogam, T. Scotti, and A. Wirgin, Retrieval of the physical properties of an anelastic solid half space from seismic data, Journal of Applied Geophysics, vol.88, pp.70-82, 2013.
DOI : 10.1016/j.jappgeo.2012.09.010

K. Mckinnon, Convergence of the Nelder--Mead Simplex Method to a Nonstationary Point, SIAM Journal on Optimization, vol.9, issue.1, pp.148-158, 1998.
DOI : 10.1137/S1052623496303482

M. Moghaddam, W. C. Chew, and M. Oristaglio, Comparison of the born iterative method and tarantola's method for an electromagnetic time-domain inverse problem, International Journal of Imaging Systems and Technology, vol.27, issue.4, pp.318-333, 1991.
DOI : 10.1002/ima.1850030405

E. Mudry, P. C. Chaumet, K. Belkebir, and A. Sentenac, Electromagnetic wave imaging of three-dimensional targets using a hybrid iterative inversion method, Inverse Problems, vol.28, issue.6, p.65007, 2012.
DOI : 10.1088/0266-5611/28/6/065007

URL : https://hal.archives-ouvertes.fr/hal-00939212

J. A. Nelder and R. Mead, A Simplex method for function minimization, The Comput, J, vol.7, pp.308-313, 1965.

Y. Niwa, S. Hirose, and M. Kitahara, Application of the boundary integral equation (BIE) method to transient response analysis of inclusions in a half space, Wave Motion, vol.8, issue.1, pp.77-91, 1986.
DOI : 10.1016/0165-2125(86)90007-7

E. Ogam, Caractérisation ultrasonore et vibroacoustique de la santé mécanique des os humains, 2007.

E. Ogam and Z. E. Fellah, The direct and inverse problems of an air-saturated poroelastic cylinder submitted to acoustic radiation, AIP Advances, vol.1, issue.3, p.32174, 2011.
DOI : 10.1063/1.3647619

URL : https://hal.archives-ouvertes.fr/hal-00626638

W. H. Press, S. A. Teukolsky, W. T. Vettering, and B. P. Flannery, Numerical Recipes in Fortran, pp.402-406, 1992.

W. Sachse, . Castagnède, I. Grabec, K. Y. Kim, and R. L. Weaver, Recent developments in quantitative ultrasonic NDE of composites, Ultrasonics, vol.28, issue.2, pp.97-104, 1990.
DOI : 10.1016/0041-624X(90)90005-9

G. Schmitz, Ultrasound in Medical Diagnosis, Academic, pp.162-174, 2002.
DOI : 10.1016/B978-012613760-6/50010-3

T. Scotti and A. Wirgin, Real-time sonomammography based on the intersecting canonical body approximation of the diffracted wave field, Ultrasonics, vol.36, issue.1-5, pp.643-652, 1998.
DOI : 10.1016/S0041-624X(97)00127-3

T. Scotti and A. Wirgin, Reconstruction of the three mechanical material constants of a lossy fluid-like cylinder from low-frequency scattered acoustic fields, Comptes Rendus M??canique, vol.332, issue.9, pp.717-724, 2004.
DOI : 10.1016/j.crme.2004.03.018

URL : https://hal.archives-ouvertes.fr/hal-00000843

N. Sebaa, Z. E. Fellah, M. Fellah, E. Ogam, F. G. Mitri et al., Application of the Biot model to ultrasound in bone: Inverse problem, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.55, issue.7, pp.1516-1523, 2008.
DOI : 10.1109/TUFFC.2008.827

URL : https://hal.archives-ouvertes.fr/hal-00326008

C. Sun, C. Chiu, C. Li, and C. H. Huang, Time Domain Image Reconstruction for Homogenous Dielectric Objects by Dynamic Differential Evolution, Electromagnetics, vol.30, issue.4, pp.309-323, 2010.
DOI : 10.1080/02726341003712491

A. Tarantola, A strategy for nonlinear elastic inversion of seismic reflection data, GEOPHYSICS, vol.51, issue.10, pp.1893-1903, 1986.
DOI : 10.1190/1.1442046

R. B. Thompson, Laboratory nondestructive evaluation technology for materials characterization, Journal of Nondestructive Evaluation, vol.22, issue.3-4, pp.163-176, 1996.
DOI : 10.1007/BF00732043

J. J. Tomick, On convergence of the Nelder-Mead simplex algorithm for unconstrained stochastic optimization, 1995.

J. Virieux and S. Operto, An overview of full-waveform inversion in exploration geophysics, GEOPHYSICS, vol.74, issue.6, pp.127-152, 2009.
DOI : 10.1190/1.3238367

URL : https://hal.archives-ouvertes.fr/hal-00457989

K. E. Vugrin, On the effects of noise on parameter identification optimization problems, 2004.

A. Wirgin, Some Quasi-Analytic and Numerical Methods for Acoustical Imaging of Complex Media, pp.241-304, 1999.
DOI : 10.1007/978-3-7091-2486-4_5

A. Wirgin, The inverse crime, p.401050, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00001084

A. Wirgin and T. Scotti, Shape Reconstruction of a Penetrable Scattering Body via Diffracted Waves and Canonical Solutions, Acoustical Imaging, vol.23, pp.459-464, 1997.
DOI : 10.1007/978-1-4419-8588-0_73

J. Wiskin, D. T. Borup, S. A. Johnson, and M. Berggren, Non-linear inverse scattering: High resolution quantitative breast tissue tomography, The Journal of the Acoustical Society of America, vol.131, issue.5, pp.3802-3813, 2012.
DOI : 10.1121/1.3699240

C. Yeh and C. Yang, Characterization of mechanical and geometrical properties of a tube with axial and circumferential guided waves, Ultrasonics, vol.51, issue.4, pp.472-479, 2011.
DOI : 10.1016/j.ultras.2010.11.013

X. Zhang, S. L. Broschat, and P. J. Flynn, A comparison of material classification techniques for ultrasound inverse imaging, The Journal of the Acoustical Society of America, vol.111, issue.1, pp.457-467, 2002.
DOI : 10.1121/1.1424869