BIBLIOGRAPHIE ETENDUE 

[1] Conjugate Gradient Method for Solving Inverse Scattering with Experimental DataP. Lobel, R. Kleinman, Ch. Pichot, L. BlancFéraud, and M. Barlaud IEEE Antennas & Propagation Magazine, Vol. 38, No 3, pp. 4851, June 1996. Article invité. The reconstruction of the complex permittivity profile of lossy dielectric objects from measured farfield data is considered, with application to perfectly conducting (PEC) objects. From an integral representation of the electric field (EFIE) and applying moment method solution, an iterative reconstruction algorithm based on a conjugate gradient method is derived. In order to start the iterative procedure with an initial guess, a backpropagation scheme is used. For testing the algorithm on real measured data, the reconstruction of two PEC (cylinder and strip) objects is presented. [2] A New Regularization Scheme for Inverse ScatteringP. Lobel, L. BlancFéraud, Ch. Pichot, and M. Barlaud Inverse Problems, vol. 13, No. 12, pp. 403410, Avril 1997. The reconstruction of the complexe permittivity profile of inhomogeneous objects from measured scattered field data is a strongly nonlinear and illposed problem. Generally, the quality of the reconstruction from noisy data is enhanced by the introduction of a regularization scheme. Starting from an iterative algorithm based on a conjugate gradient method and applied to the complete nonlinear problem, this paper deals with a new regularization scheme, using edgepreserving potential functions. With this a priori information, the object to reconstruct is modeled with homogeneous areas separated by borderlike discontinuities. The enhancement is illustrated throughout some examples with noisy synthetic data. [8] A Fast Tomographic Reconstruction Algorithm in the 2D Wavelet Transform DomainL. BlancFéraud, P. Charbonnier, P. Lobel, and M. Barlaud In International Conference on Acoustics, Speech and Signal Processing, volume V, pages 305308, Adelaide, South Australia, April 1994. Une nouvelle méthode en reconstruction tomographique utlisant une Transformée en Ondelettes 2D (TO) est proposée. La résolution de ce problème fait intervenir des calculs sur des matrices de grandes tailles, ce qui pénalise grandement la vitesse de convergence. La TO concentre toute l'information importante dans un nombre restreint de pixels. On pourra donc creuser les matrices ainsi transformées et augmenter par la même la vitesse de résolution. Travailler dans le domaine de la TO permet aussi de répartir les erreurs sur plusieurs résolutions et donc de contrôler la qualité de la reconstruction. Nous montrons de plus que la TO 2D est plus efficace que la TO 1D. [9] Different Spatial Iterative Methods For Microwave Inverse ScatteringP. Lobel, R. Kleinman, Ch. Pichot, L. BlancFéraud, and M. Barlaud In Digest USNC/URSI Radio Science Meeting, page 344, Newport Beach, California, USA, June 1995. This paper deals with a comparative study between different iterative methods for reconstruction of 2DTM objects using scattered nearfield data in the microwave domain. For this comparative study, the first iterative algorithm is based on a LevenbergMarquardt method which is a modified GaussNewton or NewtonKantorovitch method. A standard Tikhonov regularization with identity operator is used. Different strategies have been utilized for finding the regularisation parameters such as an empirical formula and the Generalized Cross Validation method. The second iterative method is based on a Gradient method. First order as well as second order approximations were taken into account successively in the algorithm. Various correction directions (standard gradient direction and PolakRibière conjugate gradient direction) were employed. [10] Object reconstruction From FarField data Using Gradient and GaussNewton Type MethodsP. Lobel, R. Kleinman, Ch. Pichot, L. BlancFéraud, and M. Barlaud In Digest USNC/URSI Radio Science Meeting, page 233, Newport Beach, California, USA, June 1995. Communication invitée. The reconstruction of 2DTM objects using measured scattered farfield data is presented in this paper. Two iterative methods have been used. The first one is based on a LevenbergMarquardt method and the second is a Gradient method. Different objects from the measured IPSWITCH data (perfectly electrically conducting target (PEC), coated PEC and penetrable target (PEN)) have been successfully reconstructed using these two methods. [11] Gradient Method For Solving Non Linear Inverse Scattering In Microwave TomographyP. Lobel, R. Kleinman, Ch. Pichot, L. BlancFéraud, and M. Barlaud In Progress In Electromagnetics Research Symposium (PIERS'95), page 742, Seattle, Washington, USA, July 1995. University of Washington. This paper deals with a new numerical iterative method for solving an inverse scattering problem: the reconstruction of complex permittivity of inhomogeneous lossy dielectric objects imbedded in a homogeneous medium from scattered near field data in the 2DTM case. The nature of this problem is strongly nonlinear and ill posed when quantitative imaging is required. The algorithm presented here, based on a gradient method, is applied to the complete nonlinear problem discretized using the moment method. The cost functional to be minimized is the normalized error matching measured scattered data. Different correction directions (standard gradient direction and PolakRibière conjugate gradient direction) have been studied. Investigations on the initial guess of the complex permittivity profile have also been made with a backpropagation scheme using the adjoint operator which allow to provide an estimate of the induce current inside inhomogeneous object. Finally, we present the enhancement in the reconstruction of noisy simulated data by the addition of a regularization term using edgepreserving potential functions PHI. [12] Conjugate Gradient Algorithm with EdgePreserving Regularization for Microwave Inverse ScatteringP. Lobel, L. BlancFéraud, Ch. Pichot, and M. Barlaud In Progress In Electromagnetics Research Symposium (PIERS'96), page 355, Innsbruck, Austria, 812 July 1996. Communication invitée An iterative algorithm based on a conjugate gradient has been recently proposed in [1,10]. However, working with strongly noisy data or trying to reconstruct large value of complex permittivity may degrade the quality of the reconstruction. A new edgepreserving regularization scheme involving potential functions is presented in this paper. Enhancement of the quality of the reconstruction is illustrated using noisy scattered data by comparaison between solutions obtained with and without regularization term. [13] Conjugate Gradient Algorithm with EdgePreserving Regularization for Image Reconstruction from Experimental DataP. Lobel, Ch. Pichot, L. BlancFéraud, and M. Barlaud In IEEE APS International Symposium, vol. 1, pp. 644647, Baltimore, Maryland, USA, July 21th26th, 1996. Communication invitée. The reconstruction of the complex permittivity profile of 2DTM objects using scattered farfield data is considered. In order to solve this nonlinear and illposed inverse scattering problem, an iterative algorithm based on a conjugate gradient method was proposed [1,10] and applied successfully on two Ipswich data sets, i.e. a metallic circular cylinder and a metallic strip [1]. In order to enhance the reconstruction in terms of convergence, stability versus signal to noise ratio, large value of complex contrast, a regularized form of the conjugate gradient method is proposed and applied on the Ipswich data sets. This paper can be downloaded here. [14] Regularized Inversion Algorithms for Microwave ImagingCh. Pichot, P. Lobel, L. BlancFéraud, and M. Barlaud In XXVth General Assembly of the International Union of Radio Science (URSI), page 74, Lille, France, August 28th  September 5th 1996. Communication invitée. This paper deals with a comparative study, using different regularized inversion algorithms. We emphasize on the influence of various regularization schemes applied to both NewtonKantorovitch and conjugate gradient method. A standart Tikhonov regularization with identity and gradient operators and an edgepreserving regularization, using potential functions have been applied. In this last and nonlinear case, we make use of an algorithm based on a semiquadratic regularization involving an explicit edge variable. [19] GaussNewton and Gradient Methods for Microwave TomographyCh. Pichot, P. Lobel, Kamal Belkebir, J.M. Elissalt, and J.M. Geffrin In Meetings at Oberwolfach on Inverse Problems in Medical Imaging and Nondestructive Testing, Oberwolfach, Germany, February 1996. Communication invitée. Publié dans Inverse Problems in Medical Imaging and Nondestructive Testing [6]. We present different iterative methods and compare their performance for soving an inverse scattering problem : the reconstruction of the complex permittivity profile of inhomogeneous dielectric objects embedded in a homogeneous medium, from near or farfield scattered data in the 2DTM case. Applications concerned here are medical imaging, nondestructive testing and target identification. [22] Reconstruction Tomographique dans le Domaine de la Transformée en Ondelettes bidimensionnelleP. Lobel, L. BlancFéraud, P. Charbonnier, and M. Barlaud Research Note 9360, Laboratoire Informatique Signaux et Systèmes de Sophia Antipolis, October 1993. Cet article s'inscrit dans le cadre de la reconstruction tomographique en imagerie médicale, qui implique la résolution de problèmes inverses faisant intervenir des matrices de grandes tailles. La passage dans l'espace Transformée en Ondelettes va rendre ces matrices très creuses, en concentrant les informations significatives dans un nombre restreint d'éléments de la matrice d'entrée. Le volume de données ainsi réduit, l'utilisation d'une algorithmique spécifique permettra d'augmenter fortement la vitesse de résolution du système. La reconstruction dans le domaine de la Transformée en Ondelettes de l'image permettra de mieux répartir les erreurs sur les différentes résolutions et ainsi d'améliorer la qualité de la reconstruction. [23] Technical Development for an EdgePreserving Regularization Method in Inverse ScatteringP. Lobel, L. BlancFéraud, Ch. Pichot, and M. Barlaud Research Note 9573, Laboratoire Informatique Signaux et Systèmes de Sophia Antipolis, December 1995. This paper deals with the adaptation of an edgepreserving regularization method to the illposed problem of inverse scattering. The reconstruction of complex permittivity of inhomogeneous objects from scattered field data, leads to a nonlinear equation. Our primary algorithm, based on a conjugate gradient method shows some limitations face to noisy corrupted data. A significant enhancement is proposed by the addition of a new regularization term. The object to be reconstructed is modeled with homogeneous areas, separated by borderlike discontinuities. Based on the use of edgepreserving potential functions, our algorithm smoothes the homogeneous areas of the solution, while preserving the reconstruction of the edges, which are important attributes of the object. This method leads to an additive nonlinear problem, and we present a usefull way to deal with it. Finally, some examples with synthetic data illustrate the enhancement brought by the method. 

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