O. Cmielewski, H. Tortel, A. Litman, and M. Saillard, A Two-Step Procedure for Characterizing Obstacles Under a Rough Surface From Bistatic Measurements, IEEE Transactions on Geoscience and Remote Sensing, vol.45, issue.9, pp.2850-2858, 2007.
DOI : 10.1109/TGRS.2007.902289

URL : https://hal.archives-ouvertes.fr/hal-00438258

L. Crocco, M. D. Urso, and T. Isernia, Faithful non-linear imaging from only-amplitude measurements of incident and total fields, Optics Express, vol.15, issue.7, pp.3804-3815, 2007.
DOI : 10.1364/OE.15.003804

L. Crocco and A. Litman, On embedded microwave imaging systems: retrievable information and design guidelines, Inverse Problems, vol.25, issue.6, pp.65001-65041, 2009.
DOI : 10.1088/0266-5611/25/6/065001

URL : https://hal.archives-ouvertes.fr/hal-00438270

F. Dresk, Imagerie optique haute résolution, p.41, 2005.

M. D. Urso, K. Belkebir, L. Crocco, T. Isernia, and A. Litman, Phaseless imaging with experimental data: facts and challenges, Journal of the Optical Society of America A, vol.25, issue.1, pp.271-281, 2008.
DOI : 10.1364/JOSAA.25.000271

URL : https://hal.archives-ouvertes.fr/hal-00438268

C. Eyraud, J. Geffrin, A. Litman, P. Sabouroux, and H. Giovannini, Drift correction for scattering measurements, Applied Physics Letters, vol.89, issue.24, pp.244104-244138, 2006.
DOI : 10.1063/1.2404978

URL : https://hal.archives-ouvertes.fr/hal-00120448

C. Eyraud, J. Geffrin, P. Sabouroux, P. C. Chaumet, H. Tortel et al., Validation of a 3D bistatic microwave scattering measurement setup, Radio Science, vol.39, issue.80, p.34, 2008.
DOI : 10.1029/2008RS003836

URL : https://hal.archives-ouvertes.fr/hal-00348506

C. Eyraud, A. Litman, A. Herique, and W. Kofman, Microwave imaging from experimental data within a Bayesian framework with realistic random noise, Inverse Problems, vol.25, issue.2, pp.24005-24039, 2009.
DOI : 10.1088/0266-5611/25/2/024005

URL : https://hal.archives-ouvertes.fr/insu-00409963

J. Geffrin, Imagerie microonde : Etude d'un scanneràscanner`scannerà 434 MHz pour applications biomédicales, p.37, 1995.

J. Geffrin, C. Eyraud, A. Litman, and P. Sabouroux, Optimization of a bistatic microwave scattering measurement setup: From high to low scattering targets, Radio Science, vol.39, issue.2, pp.2007-2041, 2009.
DOI : 10.1029/2008RS003837

URL : https://hal.archives-ouvertes.fr/hal-00355811

J. Geffrin, P. Sabouroux, and C. Eyraud, Free space experimental scattering database continuation: experimental set-up and measurement precision, Inverse Problems, vol.21, issue.6, pp.117-130, 2005.
DOI : 10.1088/0266-5611/21/6/S09

URL : https://hal.archives-ouvertes.fr/hal-00082489

R. Kleinman, P. M. Van-den, and . Berg, A modified gradient method for two- dimensional problems in tomography, Journal of Computational and Applied Mathematics, vol.42, issue.1, pp.17-35, 1992.
DOI : 10.1016/0377-0427(92)90160-Y

R. Lencrerot, Outils de modélisation et d'imagerie d'un scanner micro-onde : Application au contrôle de la teneur en eau d'une colonne de sol, p.39, 1998.

R. Lencrerot, A. Litman, H. Tortel, and J. Geffrin, Measurement strategies for a confined microwave circular scanner, Inverse Problems in Science and Engineering, vol.17, issue.6, pp.357869-357909, 2009.
DOI : 10.1080/17415970802577012

URL : https://hal.archives-ouvertes.fr/hal-00438249

R. Lencrerot, A. Litman, H. Tortel, and J. Geffrin, A microwave imaging circular setup for soil moisture information, 2007 IEEE International Geoscience and Remote Sensing Symposium, pp.4394-4397, 2007.
DOI : 10.1109/IGARSS.2007.4423827

URL : https://hal.archives-ouvertes.fr/hal-00486823

A. Litman, -ary scattering obstacles, Inverse Problems, vol.21, issue.6, pp.131-152, 2005.
DOI : 10.1088/0266-5611/21/6/S10

URL : https://hal.archives-ouvertes.fr/hal-00857572

A. Litman and K. Belkebir, Two-dimensional inverse profiling problem using phaseless data, Journal of the Optical Society of America A, vol.23, issue.11, pp.2737-2746, 2006.
DOI : 10.1364/JOSAA.23.002737

URL : https://hal.archives-ouvertes.fr/hal-00082943

A. Litman and L. Crocco, Testing inversion algorithms against experimental data: 3D targets, Inverse Problems, vol.25, issue.2, pp.20201-20235, 2009.
DOI : 10.1088/0266-5611/25/2/020201

M. Masmoudi, J. Pommier, and B. Samet, The topological asymptotic expansion for the Maxwell equations and some applications, Inverse Problems, vol.21, issue.2, pp.547-564, 2005.
DOI : 10.1088/0266-5611/21/2/008

M. Serhir, J. Geffrin, A. Litman, and P. Besnier, Aperture antenna modelling by a finite number of elemental dipoles from spherical field measurements

A. G. Tijhuis, K. Belkebir, A. Litman, and B. P. De-hon, Multiple-frequency distortedwave born approach to 2D inverse profiling, Inverse Problems, vol.21, pp.1635-1644, 2001.
DOI : 10.1088/0266-5611/17/6/307

URL : https://hal.archives-ouvertes.fr/hal-00081631

A. G. Tijhuis, K. Belkebir, A. Litman, and B. P. De-hon, Theoretical and computational aspects of 2-D inverse profiling, IEEE Transactions on Geoscience and Remote Sensing, vol.39, issue.6, pp.1316-1330, 2001.
DOI : 10.1109/36.927455

G. Topp, J. Davis, and A. Annan, Electromagnetic determination of soil water content: Measurements in coaxial transmission lines, Water Resources Research, vol.16, issue.2, pp.574-582, 1980.
DOI : 10.1029/WR016i003p00574

O. Dorn and D. Lesselier, Level set methods for inverse scattering, Inverse Problems, vol.22, issue.4, pp.67-131, 2006.
DOI : 10.1088/0266-5611/22/4/R01

URL : https://hal.archives-ouvertes.fr/hal-00637348

C. Eyraud, A. Litman, A. Herique, and W. Kofman, Microwave imaging from experimental data within a Bayesian framework with realistic random noise, Inverse Problems, vol.25, issue.2, pp.24005-24051, 2009.
DOI : 10.1088/0266-5611/25/2/024005

URL : https://hal.archives-ouvertes.fr/insu-00409963

J. Geffrin, P. Sabouroux, and C. Eyraud, Free space experimental scattering database continuation: experimental set-up and measurement precision, Inverse Problems, vol.21, issue.6, pp.117-130, 2005.
DOI : 10.1088/0266-5611/21/6/S09

URL : https://hal.archives-ouvertes.fr/hal-00082489

R. Lencrerot, A. Litman, H. Tortel, and J. Geffrin, Measurement strategies for a confined microwave circular scanner, Inverse Problems in Science and Engineering, vol.17, issue.6, pp.357869-357915, 2009.
DOI : 10.1080/17415970802577012

URL : https://hal.archives-ouvertes.fr/hal-00438249

R. Lencrerot, A. Litman, H. Tortel, and J. Geffrin, Imposing Zernike representation for imaging two-dimensional targets, Inverse Problems, vol.25, issue.3, pp.35012-35060, 2009.
DOI : 10.1088/0266-5611/25/3/035012

URL : https://hal.archives-ouvertes.fr/hal-00438246

A. Litman, -ary scattering obstacles, Inverse Problems, vol.21, issue.6, pp.131-152, 2005.
DOI : 10.1088/0266-5611/21/6/S10

URL : https://hal.archives-ouvertes.fr/hal-00857572

A. Litman and K. Belkebir, Two-dimensional inverse profiling problem using phaseless data, Journal of the Optical Society of America A, vol.23, issue.11, pp.2737-2746, 2006.
DOI : 10.1364/JOSAA.23.002737

URL : https://hal.archives-ouvertes.fr/hal-00082943

A. Litman, R. Lencrerot, and J. Geffrin, Combining spatial support information and shape-based method for tomographic imaging inside a microwave cylindrical scanner, Inverse Problems in Science and Engineering, vol.1, issue.1, p.54, 2009.
DOI : 10.1088/0266-5611/24/3/035015

URL : https://hal.archives-ouvertes.fr/hal-00453662

A. Litman and D. Lesselier, On attenuation-matched inversion methods of diffusive wavefields, Inverse Problems, vol.15, issue.1, pp.99-111, 1999.
DOI : 10.1088/0266-5611/15/1/014

URL : https://hal.archives-ouvertes.fr/hal-00438281

A. Litman, D. Lesselier, and F. Santosa, Reconstruction of a two-dimensional binary obstacle by controlled evolution of a level-set, Inverse Problems, vol.14, issue.3, pp.685-706, 1998.
DOI : 10.1088/0266-5611/14/3/018

URL : https://hal.archives-ouvertes.fr/hal-00438279

J. Nocedal and S. Wright, Numerical optimization, p.47, 2006.
DOI : 10.1007/b98874

S. Osher and J. A. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, vol.79, issue.1, pp.2-49, 1988.
DOI : 10.1016/0021-9991(88)90002-2

N. Ostrowsky, D. Sornette, P. Parker, and E. R. Pike, Exponential Sampling Method for Light Scattering Polydispersity Analysis, Optica Acta: International Journal of Optics, vol.4, issue.8, pp.1059-1070, 1981.
DOI : 10.1080/713820704

F. Santosa, A level-set approach for inverse problems involving obstacles. ESAIM : Control, Optimisation and Calculus of Variations, pp.17-33, 1996.

J. Sokolowski and J. Zolésio, Introduction to Shape Optimization. Shape Sensitivity Analysis, p.52, 1992.

A. G. Tijhuis, K. Belkebir, A. Litman, and B. P. De-hon, Multiple-frequency distortedwave born approach to 2D inverse profiling, Inverse Problems, vol.21, pp.1635-1644, 2001.
URL : https://hal.archives-ouvertes.fr/hal-00081631

A. G. Tijhuis, K. Belkebir, A. Litman, and B. P. De-hon, Theoretical and computational aspects of 2-D inverse profiling, IEEE Transactions on Geoscience and Remote Sensing, vol.39, issue.6, pp.1316-1330, 2001.
DOI : 10.1109/36.927455

L. Vese and T. Chan, A multiphase level-set framework for image segmentation using the mumford and shah model, International Journal of Computer Vision, vol.50, issue.3, pp.271-293, 2002.
DOI : 10.1023/A:1020874308076

R. 1. Griffiths and R. , Optimal evaluation of formation resistivities using array induction and array laterolog tools, paper BBB presented at the 2000 SPWLA Annual Logging Symposium, pp.4-7

R. Griffiths, Better saturation from new array laterolog, " paper DDD presented at the 1999 SPWLA Annual Logging Symposium

T. Barber, Interpreting multi-array induction logs in difficult environments, " paper YY presented at the 1999 SPWLA Annual Logging Symposium

T. Barber and R. A. Rosthal, Using a Multiarray Induction Tool To Achieve High-Resolution Logs With Minimum Environmental Effects, SPE Annual Technical Conference and Exhibition, pp.6-9
DOI : 10.2118/22725-MS

J. D. Klein, The petrophysics of electrically anisotropic reservoirs , " paper HH presented at the 1995 SPWLA Annual Logging Symposium, pp.26-29

L. Jammes, Improved Saturation Determination in Thin-Bed Environments Using 2D Parametric Inversion, SPE Annual Technical Conference and Exhibition, pp.1-4
DOI : 10.2118/62907-MS

A. G. Mezzatesta, Integrated 2D interpretation of resistivity logging measurements by inversion methods, " paper E presented at the 1995 SPWLA Annual Logging Symposium, pp.26-29

M. A. Frenkel, Minimum and maximum pay estimation using resistivity log data inversion, " paper Z presented at the 1998 SPWLA Annual Logging Symposium, pp.26-29

I. M. Warrilow, Application of Resistivity Inversion Software to Thin-Bed Evaluation, " paper SPE 29263 presented at the 1995 SPE Asia Pacific Oil and Gas Conference, pp.20-22

Z. Zhang, Petrophysically constrained inversion of resistivity logging data, Petrophysics, vol.43, issue.2, 2002.

M. Gonfalini and M. T. Galli, Array Induction measurements in complex environments: a comparison between AIT* and HDIL** responses, SPE Annual Technical Conference and Exhibition
DOI : 10.2118/71711-MS

F. M. Haynes, Applications of resistivity modeling in reservoir development: examples from Balder Field, Norwegian North Sea, Petrophysics, vol.41, issue.4, 2000.

J. Smits, High Resolution From a New Laterolog With Azimuthal Imaging, SPE Annual Technical Conference and Exhibition, pp.22-25
DOI : 10.2118/30584-MS

J. Smits, Improved Resistivity Interpretation Utilizing a New Array Laterolog Tool and Associated Inversion Processing, " paper SPE 49328 prepared for presentation at the, SPE Annual Technical Conference and Exhibition, pp.27-30, 1998.

V. Dussan, Estimating vertical permeability from resistivity logs, " paper UU presented at the 1994 SPWLA Annual Logging Symposium, pp.19-22

N. Bona, Use of an Integrated Approach for Estimating Petrophysical Properties in a Complex Fractured Reservoir: A Case History, SPE Annual Technical Conference and Exhibition
DOI : 10.2118/71741-MS

P. Gossenberg, Practical applications of resistivity modelling techniques in clastic reservoirs, " paper 110 presented at the OMC, pp.26-28, 2003.

R. and .. V. Lauer, New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope, Journal of Microscopy, vol.205, issue.2, pp.165-176, 2002.
DOI : 10.1046/j.0022-2720.2001.00980.x

URL : https://hal.archives-ouvertes.fr/hal-00869524

N. Destouches, C. A. Guérin, M. Lequime, and H. Giovannini, Determination of the phase of the diffracted field in the optical domain, Optics Communications, vol.198, issue.4-6, pp.233-239, 2001.
DOI : 10.1016/S0030-4018(01)01478-X

URL : https://hal.archives-ouvertes.fr/hal-00083206

G. Gbur and E. Wolf, The information content of the scattered intensity in diffraction tomography, Information Sciences, vol.162, issue.1, pp.3-20, 2004.
DOI : 10.1016/j.ins.2003.01.001

K. Belkebir and M. Saillard, Special section: testing inversion algorithms against experimental data: inhomogeneous targets Inverse Problems 21, pp.1-3, 2005.

A. Litman and L. Crocco, Testing inversion algorithms against experimental data: 3D targets, Inverse Problems, vol.25, issue.2, p.20201, 2009.
DOI : 10.1088/0266-5611/25/2/020201

F. Soldovieri, R. Persico, and G. Leone, Effect of source and receiver radiation characteristics in subsurface prospecting within the DBA Radio Sci, pp.40-3006, 2005.

J. Geffrin, Imagerie microonde: etude d'un scanner a 434 MHz pour des applications biomedicales PhD thesis, 1995.

R. Lencrerot, A. Litman, H. Tortel, and J. Geffrin, A microwave imaging circular setup for soil moisture information, 2007 IEEE International Geoscience and Remote Sensing Symposium, pp.4394-4401, 2007.
DOI : 10.1109/IGARSS.2007.4423827

URL : https://hal.archives-ouvertes.fr/hal-00486823

L. Jofre, M. S. Hawley, A. Broquetas, R. E. De-los, M. Ferrando et al., Medical imaging with a microwave tomographic scanner, IEEE Transactions on Biomedical Engineering, vol.37, issue.3, pp.303-314, 1990.
DOI : 10.1109/10.52331

P. M. Meaney, K. D. Paulsen, A. Hartov, and R. Crane, An active microwave imaging system for reconstruction of 2-D electrical property distributions, IEEE Transactions on Biomedical Engineering, vol.42, issue.10, pp.1017-1042, 1995.
DOI : 10.1109/10.464376

A. Broquetas, J. Romeu, J. M. Rius, A. R. Elias-fuste, A. Cardama et al., Cylindrical geometry: a further step in active microwave tomography, IEEE Transactions on Microwave Theory and Techniques, vol.39, issue.5, pp.836-880, 1991.
DOI : 10.1109/22.79111

A. Franchois and A. Tijhuis, A quasi-newton reconstruction algorithm for a complex microwave imaging scanner environment Radio Sci, p.8011, 2003.

P. Van-den-berg and J. Fokkema, Removal of undesired wavefields related to the casing of a microwave scanner, IEEE Transactions on Microwave Theory and Techniques, vol.51, issue.1, pp.187-92, 2003.
DOI : 10.1109/TMTT.2002.806900

A. G. Tijhuis and A. Franchois, A two-dimensional microwave imaging algorithm for a complex environment: preliminary results, Proc. URSI Int. Electromagnetic Theory Symp, pp.445-452, 2001.

O. Bucci and I. , Electromagnetic inverse scattering: Retrievable information and measurement strategies, Radio Science, vol.29, issue.6, pp.2123-2161, 1997.
DOI : 10.1029/97RS01826

R. Porter and A. J. Devaney, Generalized holography and computational solutions to inverse source problems, Journal of the Optical Society of America, vol.72, issue.12, pp.1707-1720, 1982.
DOI : 10.1364/JOSA.72.001707

O. M. Bucci, L. Crocco, and T. Isernia, Improving the reconstruction capabilities in inverse scattering problems by exploitation of close-proximity setups, Journal of the Optical Society of America A, vol.16, issue.7, pp.1788-98, 1999.
DOI : 10.1364/JOSAA.16.001788

A. Brancaccio, G. Leone, and R. Pierri, Information content of Born scattered fields: results in the circular cylindrical case, Journal of the Optical Society of America A, vol.15, issue.7, pp.1909-1926, 1998.
DOI : 10.1364/JOSAA.15.001909

R. Pierri, R. Persico, and R. Bernini, Information content of the Born field scattered by an embedded slab: multifrequency, multiview, and multifrequency???multiview cases, Journal of the Optical Society of America A, vol.16, issue.10, pp.2392-2401, 1999.
DOI : 10.1364/JOSAA.16.002392

O. M. Bucci, L. Crocco, T. Isernia, and P. , Subsurface inverse scattering problems: quantifying, qualifying, and achieving the available information, IEEE Transactions on Geoscience and Remote Sensing, vol.39, issue.11, pp.2527-2565, 2001.
DOI : 10.1109/36.964991

A. J. Devaney, E. A. Marengo, and M. Li, Inverse Source Problem in Nonhomogeneous Background Media, SIAM Journal on Applied Mathematics, vol.67, issue.5, pp.1353-78, 2007.
DOI : 10.1137/060658618

M. R. Khodja and E. A. Marengo, Radiation enhancement due to metamaterial substrates from an inverse source theory Phys. Rev, p.46605, 2008.

S. Nordebo, M. Gustafsson, and B. Nilsson, Fisher information analysis for two-dimensional microwave tomography, Inverse Problems, vol.23, issue.3, pp.859-77, 2007.
DOI : 10.1088/0266-5611/23/3/001

O. M. Bucci, N. Cardace, L. Crocco, and I. , Degree of nonlinearity and a new solution procedure in scalar two-dimensional inverse scattering problems, Journal of the Optical Society of America A, vol.18, issue.8, pp.1832-1875, 2001.
DOI : 10.1364/JOSAA.18.001832

O. M. Bucci, N. Cardace, L. Crocco, and T. Isernia, 2D inverse scattering: degree of nonlinearity, solution strategies, and polarization effects, Image Reconstruction from Incomplete Data, pp.185-195, 2000.
DOI : 10.1117/12.409269

O. M. Bucci, A. Capozzoli, D. Elia, and G. , A novel approach to scatterers localization problem, IEEE Transactions on Antennas and Propagation, vol.51, issue.8, pp.2079-90, 2003.
DOI : 10.1109/TAP.2003.812233

R. Lencrerot, A. Litman, H. Tortel, and J. Geffrin, A microwave imaging circular setup for soil moisture information IGARSS Conf, Proc. pp, pp.4394-4401, 2007.

O. Bucci and I. , Electromagnetic inverse scattering: Retrievable information and measurement strategies, Radio Science, vol.29, issue.6, pp.2123-2161, 1997.
DOI : 10.1029/97RS01826

D. Urso, M. Belkebir, K. Crocco, L. Isernia, T. Litman et al., Phaseless imaging with experimental data: facts and challenges, Journal of the Optical Society of America A, vol.25, issue.1, pp.271-81, 2008.
DOI : 10.1364/JOSAA.25.000271

URL : https://hal.archives-ouvertes.fr/hal-00438268

T. Isernia, V. Pascazio, and R. Pierri, On the local minima in a tomographic imaging technique, IEEE Transactions on Geoscience and Remote Sensing, vol.39, issue.7, pp.1596-607, 2001.
DOI : 10.1109/36.934091

A. Baussard, E. Miller, and D. Premel, -spline scheme for solving an inverse scattering problem, Inverse Problems, vol.20, issue.2, pp.347-65, 2004.
DOI : 10.1088/0266-5611/20/2/003

URL : https://hal.archives-ouvertes.fr/hal-00636368

E. Miller and A. Willsky, Wavelet-based methods for the nonlinear inverse scattering problem using the extended born approximation Radio Sci, pp.51-66, 1996.

O. M. Bucci, L. Crocco, and T. Isernia, Improving the reconstruction capabilities in inverse scattering problems by exploitation of close-proximity setups, Journal of the Optical Society of America A, vol.16, issue.7, pp.1788-98, 1999.
DOI : 10.1364/JOSAA.16.001788

L. Crocco and A. Litman, On embedded microwave imaging systems: retrievable information and design guidelines, Inverse Problems, vol.25, issue.6, 2008.
DOI : 10.1088/0266-5611/25/6/065001

URL : https://hal.archives-ouvertes.fr/hal-00438270

C. Cerjan, Zernike-Bessel representation and its application to Hankel transforms, Journal of the Optical Society of America A, vol.24, issue.6, pp.1609-1625, 2007.
DOI : 10.1364/JOSAA.24.001609

Q. Fang, P. M. Meaney, and K. Paulsen, Singular Value Analysis of the Jacobian Matrix in Microwave Image Reconstruction, IEEE Transactions on Antennas and Propagation, vol.54, issue.8, pp.2371-80, 2006.
DOI : 10.1109/TAP.2006.879192

M. Teague, Image analysis via the general theory of moments*, Journal of the Optical Society of America, vol.70, issue.8, pp.920-950, 1980.
DOI : 10.1364/JOSA.70.000920

T. Xia, H. Zhu, H. Shu, P. Haigron, and L. Luo, Image description with generalized pseudo-Zernike moments, Journal of the Optical Society of America A, vol.24, issue.1, pp.50-59, 2007.
DOI : 10.1364/JOSAA.24.000050

URL : https://hal.archives-ouvertes.fr/inserm-00133663

J. Geffrin, Imagerie microonde: Etude d'un scanner a 434 MHz pour applications biomedicales PhD Thesis, 1995.

A. G. Tijhuis and A. Franchois, A two-dimensional microwave imaging algorithm for a complex environment, Proc. URSI Int. Electromagnetic Theory Symp, pp.445-452, 2001.

P. Van-den-berg and J. Fokkema, Removal of undesired wavefields related to the casing of a microwave scanner, IEEE Transactions on Microwave Theory and Techniques, vol.51, issue.1, pp.187-92, 2003.
DOI : 10.1109/TMTT.2002.806900

O. Cmielewski, H. Tortel, A. Litman, and M. Saillard, A Two-Step Procedure for Characterizing Obstacles Under a Rough Surface From Bistatic Measurements, IEEE Transactions on Geoscience and Remote Sensing, vol.45, issue.9, pp.2850-2858, 2007.
DOI : 10.1109/TGRS.2007.902289

URL : https://hal.archives-ouvertes.fr/hal-00438258

C. Geuzaine and J. Remacle, Gmsh reference manual: a three-dimensional finite element mesh generator with built-in pre-and post-processing facilities, Technical Report, 2007.

J. W. Demmel, S. C. Eisenstat, J. R. Gilbert, X. Li, and J. Liu, A Supernodal Approach to Sparse Partial Pivoting, SIAM Journal on Matrix Analysis and Applications, vol.20, issue.3, pp.720-55, 1999.
DOI : 10.1137/S0895479895291765

R. Lencrerot, Outils de modélisation et d'imagerie pour un scanner micro-onde: Application au contrôle de la teneur en eau d'une colonne de sol, 2008.

G. Tyras, Radiation and Propagation of Electromagnetic Waves, 1970.

A. Joisel, J. M. Geffrin, J. M. Elissalt, K. Belkebir, N. Joachimowicz et al., Iterative 2D reconstruction algorithms for microwave active imaging systems, IEE Colloquium Appl. Microwaves Medecine, vol.28, pp.9-10, 1995.
DOI : 10.1049/ic:19950260

A. Franchois and A. Tijhuis, A quasi-Newton reconstruction algorithm for a complex microwave imaging scanner environment Radio Sci, p.8011, 2003.
DOI : 10.1029/2001rs002590

URL : http://repository.tue.nl/680396

A. Litman and K. Belkebir, Two-dimensional inverse profiling problem using phaseless data, Journal of the Optical Society of America A, vol.23, issue.11, pp.2737-2783, 2006.
DOI : 10.1364/JOSAA.23.002737

URL : https://hal.archives-ouvertes.fr/hal-00082943

C. Pichot, A. Franchois, A. Joisel, and J. Bolomey, Quantitative microwave imaging with a 2.45-GHz planar microwave antenna IEEET rans, Med.Imag, vol.17, pp.550-61, 1998.
URL : https://hal.archives-ouvertes.fr/hal-00986841

O. Bucci, C. Gennarelli, and C. Savarese, Representation of electromagnetic fields over arbitrary surfaces by a finite and nonredundant number of samples, IEEE Transactions on Antennas and Propagation, vol.46, issue.3, pp.351-360, 1998.
DOI : 10.1109/8.662654

H. Micolau, H. Tortel, and M. Saillard, Decomposition of the time reversal operator for electromagnetic scattering, J. Electromagn. Waves Appl, vol.13, pp.687-719, 1999.
URL : https://hal.archives-ouvertes.fr/hal-00082837

P. Sabouroux and P. Boschi, Epsimu: a new microwave materials measurement kit Revue de l'Electricité et de l, Electronique, vol.10, pp.58-62, 2005.

A. Litman, R. Lencrerot, H. Tortel, and J. Geffrin, Level-set imaging in a metallic cylindrical cavity configuration Inverse Problems: Modeling and Simulation Conf, pp.114-119, 2008.

T. Dogaru and L. Carin, Time-domain sensing of targets buried under a rough air-ground interface, IEEE Transactions on Antennas and Propagation, vol.46, issue.3, pp.360-372, 1998.
DOI : 10.1109/8.662655

T. Dogaru, L. Collins, and L. Carin, Optimal time-domain detection of a deterministic target buried under a randomly rough interface, IEEE Transactions on Antennas and Propagation, vol.49, issue.3, pp.313-326, 2001.
DOI : 10.1109/8.918604

T. Dogaru and L. Carin, Time-domain sensing of targets buried under a Gaussian, exponential, or fractal rough interface, IEEE Transactions on Geoscience and Remote Sensing, vol.39, issue.8
DOI : 10.1109/36.942559

P. D. Gader, M. Mystkowski, and Y. Zhao, Landmine detection with ground penetrating radar using hidden Markov models, IEEE Transactions on Geoscience and Remote Sensing, vol.39, issue.6
DOI : 10.1109/36.927446

L. Carin and E. , Foreword?Special issue on new advances in subsurface sensing: Systems modeling, and signal processing, IEEE Trans. Geosci

S. Vitebskiy, K. Sturgess, and L. Carin, Short-pulse plane-wave scattering from buried perfectly conducting bodies of revolution, IEEE Transactions on Antennas and Propagation, vol.44, issue.2, pp.143-151, 1996.
DOI : 10.1109/8.481640

S. Vitebskiy and L. Carin, Resonances of perfectly conducting wires and bodies of revolution buried in a lossy dispersive half-space, IEEE Transactions on Antennas and Propagation, vol.44, issue.12, pp.1575-1583, 1996.
DOI : 10.1109/8.546243

C. Chen and L. Peters, Buried unexploded ordnance identification via complex natural resonances, IEEE Transactions on Antennas and Propagation, vol.45, issue.11, pp.1645-1654, 1997.
DOI : 10.1109/8.650076

V. Galdi, D. Castanon, and L. Felsen, Multifrequency reconstruction of moderately rough interfaces via quasi-ray Gaussian beams, IEEE Transactions on Geoscience and Remote Sensing, vol.40, issue.2
DOI : 10.1109/36.992810

I. Catapano, L. Crocco, and T. Isernia, A simple two-dimensional inversion technique for imaging homogeneous targets in stratified media, Radio Science, vol.22, issue.4, p.1012, 2004.
DOI : 10.1029/2003RS002917

R. Firoozabadi, E. Miller, C. Rappaport, and A. Morgenthaler, Subsurface Sensing of Buried Objects Under a Randomly Rough Surface Using Scattered Electromagnetic Field Data, IEEE Transactions on Geoscience and Remote Sensing, vol.45, issue.1, pp.104-117, 2007.
DOI : 10.1109/TGRS.2006.883462

V. Galdi, H. Feng, D. A. Castanon, W. C. Carl, and L. B. Felsen, Moderately rough surface underground imaging via short-pulse quasi-ray gaussian beams, IEEE Transactions on Antennas and Propagation, vol.51, issue.9, pp.2304-2318, 2003.
DOI : 10.1109/TAP.2003.816363

A. Schatzberg and A. J. Devananey, Rough surface inverse scattering within the Rytov approximation, Journal of the Optical Society of America A, vol.10, issue.5, pp.942-950, 1993.
DOI : 10.1364/JOSAA.10.000942

R. J. Wonbell and J. A. Desanto, Reconstruction of rough-surface profiles with the Kirchhoff approximation, J. Opt. Soc. Amer. A, Opt

M. El-shenawee and E. Miller, Multiple-incidence and multifrequency for profile reconstruction of random rough surfaces using the 3-D electromagnetic fast multipole model, IEEE Transactions on Geoscience and Remote Sensing, vol.42, issue.11, pp.2499-2510, 2004.
DOI : 10.1109/TGRS.2004.834762

O. Cmielewski, M. Saillard, and H. Tortel, Detection of buried objects beneath a rough surface, Waves Random Complex Media, pp.417-431, 2006.
DOI : 10.1109/36.142943

URL : https://hal.archives-ouvertes.fr/hal-00453652

O. Cmielewski, K. Belkebir, M. Saillard, and H. Tortel, On the Characterization of Buried Targets Under a Rough Surface Using the Wigner???Ville Transformation, IEEE Geoscience and Remote Sensing Letters, vol.3, issue.4, pp.442-446, 2006.
DOI : 10.1109/LGRS.2006.874165

URL : https://hal.archives-ouvertes.fr/hal-00453653

A. Litman, D. Lesselier, and F. Santosa, Reconstruction of a two-dimensional binary obstacle by controlled evolution of a level-set, Inverse Problems, vol.14, issue.3, pp.685-706, 1998.
DOI : 10.1088/0266-5611/14/3/018

URL : https://hal.archives-ouvertes.fr/hal-00438279

O. Dorn and D. Lesselier, Level set methods for inverse scattering, Inverse Problems, vol.22, issue.4, pp.67-131, 2006.
DOI : 10.1088/0266-5611/22/4/R01

URL : https://hal.archives-ouvertes.fr/hal-00637348

J. Sethian, Level Set Methods and Fast Marching Methods,s e r, Cambridge Monographs on Applied and Computational Mathematics. Cambridge, U.K, 1999.

X. Li, W. Yan, and C. Chan, Numerical schemes for Hamilton-Jacobi equations on unstructured meshes, Numerische Mathematik, vol.94, issue.2, pp.315-331, 2003.
DOI : 10.1007/s00211-002-0418-9

X. Li and C. Chan, High-order schemes for Hamilton???Jacobi equations on triangular meshes, Journal of Computational and Applied Mathematics, vol.167, issue.1, pp.227-241, 2004.
DOI : 10.1016/j.cam.2003.09.051

S. O. Rice, Reflection of electromagnetic waves from slightly rough surfaces, The Theory of Electromagnetic Waves, 1963.
DOI : 10.1002/cpa.3160040206

F. Santosa, A level-set approach for inverse problems involving obstacles Fadil SANTOSA, ESAIM: Control, Optimisation and Calculus of Variations, vol.1, pp.17-33, 1996.
DOI : 10.1051/cocv:1996101

O. Dorn, E. L. Miller, and C. M. Rappaport, A shape reconstruction method for electromagnetic tomography using adjoint fields and level sets, Inverse Problems, vol.16, issue.5, pp.1119-1156, 2000.
DOI : 10.1088/0266-5611/16/5/303

C. Ramananjaona, M. Lambert, D. Lesselier, and J. Zolésio, Shape reconstruction of buried obstacles by controlled evolution of a level set: from a min-max formulation to numerical experimentation, Inverse Problems, vol.17, issue.4, pp.1087-1111, 2001.
DOI : 10.1088/0266-5611/17/4/335

M. Burger, Levenberg???Marquardt level set methods for inverse obstacle problems, Inverse Problems, vol.20, issue.1, pp.259-282, 2004.
DOI : 10.1088/0266-5611/20/1/016

A. Litman, -ary scattering obstacles, Inverse Problems, vol.21, issue.6, pp.131-152, 2005.
DOI : 10.1088/0266-5611/21/6/S10

URL : https://hal.archives-ouvertes.fr/hal-00857572

Y. Altuncu, A. Yapar, and I. Akduman, On the scattering of electromagnetic waves by bodies buried in a half-space with locally rough interface, IEEE Transactions on Geoscience and Remote Sensing, vol.44, issue.6, pp.1435-1443, 2006.
DOI : 10.1109/TGRS.2006.870436

D. Lawrence and K. Sarabandi, Electromagnetic scattering from a dielectric cylinder buried beneath a slightly rough surface, IEEE Transactions on Antennas and Propagation, vol.50, issue.10, pp.1368-1376, 2002.
DOI : 10.1109/TAP.2002.802160

M. Saillard and G. Toso, Electromagnetic scattering from bounded or infinite subsurface bodies, Radio Science, vol.4, issue.4, pp.1347-1360, 1997.
DOI : 10.1029/97RS00711

J. Jin, The Finite Element Method in Electromagnetics, 2002.

C. Geuzaine and J. Remacle, Gmsh: A Three Dimensional Finite Element Mesh Generator

P. R. Amestoy, I. S. Duff, and J. Excellent, Multifrontal parallel distributed symmetric and unsymmetric solvers, Computer Methods in Applied Mechanics and Engineering, vol.184, issue.2-4, pp.501-520, 2000.
DOI : 10.1016/S0045-7825(99)00242-X

URL : https://hal.archives-ouvertes.fr/hal-00856651

D. Forsyth and J. Ponce, Computer Vision?A Modern Approach, 2002.
URL : https://hal.archives-ouvertes.fr/hal-01063327

W. Rucklidge, Efficient Visual Recognition Using the Hausdorff Distance, ser, Lecture Notes in Computer Science, vol.1173, 1996.

H. B. Ameur, M. Burger, and B. Hackl, Level set methods for geometric inverse problems in linear elasticity, Inverse Problems, vol.20, issue.3, pp.673-696, 2004.
DOI : 10.1088/0266-5611/20/3/003

G. Allaire, F. Jouve, and A. Toader, Structural optimization using sensitivity analysis and a level-set method, Journal of Computational Physics, vol.194, issue.1, pp.363-93, 2004.
DOI : 10.1016/j.jcp.2003.09.032

S. Bonnard, P. Vincent, and M. Saillard, Cross-borehole inverse scattering using a boundary finite-element method, Inverse Problems, vol.14, issue.3, pp.521-555, 1998.
DOI : 10.1088/0266-5611/14/3/009

M. Burger, Levenberg???Marquardt level set methods for inverse obstacle problems, Inverse Problems, vol.20, issue.1, pp.259-82, 2004.
DOI : 10.1088/0266-5611/20/1/016

M. Burger, B. Hackl, and W. Ring, Incorporating topological derivatives into level set methods, Journal of Computational Physics, vol.194, issue.1, pp.344-62, 2004.
DOI : 10.1016/j.jcp.2003.09.033

T. Chan and X. Tai, Level set and total variation regularization for elliptic inverse problems with discontinuous coefficients, Journal of Computational Physics, vol.193, issue.1, pp.40-66, 2003.
DOI : 10.1016/j.jcp.2003.08.003

O. Dorn, E. Miller, and C. Rappaport, A shape reconstruction method for electromagnetic tomography using adjoint fields and level sets Inverse Problems, pp.1119-56, 2000.

J. M. Geffrin, P. Sabouroux, and C. Eyraud, Free space experimental scattering database continuation: experimental setup and measurement precision Inverse Problems 21, pp.117-147, 2005.

J. Gomez and O. Faugeras, Reconciling Distance Functions and Level Sets, Journal of Visual Communication and Image Representation, vol.11, issue.2, pp.209-232, 2000.
DOI : 10.1006/jvci.1999.0439

P. Guillaume and K. Sididris, The Topological Asymptotic Expansion for the Dirichlet Problem, SIAM Journal on Control and Optimization, vol.41, issue.4, pp.1042-72, 2002.
DOI : 10.1137/S0363012901384193

R. Kleinman and P. Van-den-berg, A modified gradient method for two- dimensional problems in tomography, Journal of Computational and Applied Mathematics, vol.42, issue.1, pp.17-35, 1992.
DOI : 10.1016/0377-0427(92)90160-Y

J. Lie, M. Lysaker, and X. Tai, A variant of the level set method and applications to image segmentation CAM, 2003.

J. Lie, M. Lysaker, and X. Tai, A binary level set model and some applications to Mumford?Shah image segmentation. CAM Report 04-31 UCLA Litman A, Lesselier D and Santosa F 1998 Reconstruction of a two-dimensional binary obstacle by controlled evolution of a level-set, Inverse Problems, vol.14, pp.685-706, 2004.

S. Osher and J. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, vol.79, issue.1, pp.12-49, 1988.
DOI : 10.1016/0021-9991(88)90002-2

C. Ramananjaona, M. Lambert, D. Lesselier, and J. Zolésio, Shape reconstruction of buried obstacles by controlled evolution of a level set: from a min?max formulation to numerical experimentation Inverse Problems, pp.1087-111, 2001.

C. Rozier, D. Lesselier, T. Angell, and R. Kleinmann, Shape retreival of an obstacle immersed in shallow water from a single frequency fields using a complete family method Inverse Problems, pp.487-508, 1997.

C. Samson, L. Blanc-feraud, G. Aubert, and J. Zerubia, A Level Set Model for Image Classification, Int. J. Comput. Vis, vol.40, pp.187-98, 2000.
DOI : 10.1007/3-540-48236-9_27

L. Souriau, B. Duchene, D. Lesselier, and R. Kleinmann, A modified gradient approach to inverse scattering for binary objects in stratified media Inverse Problems, pp.463-81, 1996.

X. Tai and C. T. , A survey on multiple level set methods with applications for identifying piecewise constant functions, Int. J. Numer. Anal. Model, vol.1, pp.25-47, 2004.

L. Vese and C. T. , A multiphase level set framework for image segmentation using the Mumford and Shah model Int, International Journal of Computer Vision, vol.50, issue.3, pp.271-93, 2002.
DOI : 10.1023/A:1020874308076

M. Wang and X. Wang, ???Color??? level sets: a multi-phase method for structural topology optimization with multiple materials, Computer Methods in Applied Mechanics and Engineering, vol.193, issue.6-8, pp.469-96, 2004.
DOI : 10.1016/j.cma.2003.10.008

H. Zhao, T. Chan, B. Merriman, and S. Osher, A Variational Level Set Approach to Multiphase Motion, Journal of Computational Physics, vol.127, issue.1, pp.179-95, 1996.
DOI : 10.1006/jcph.1996.0167

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.25.3048