BIBLIOGRAPHIE ETENDUE

 

[1] Conjugate Gradient Method for Solving Inverse Scattering with Experimental Data

P. Lobel, R. Kleinman, Ch. Pichot, L. Blanc-Féraud, and M. Barlaud

IEEE Antennas & Propagation Magazine, Vol. 38, No 3, pp. 48--51, June 1996. Article invité.

The reconstruction of the complex permittivity profile of lossy dielectric objects from measured far-field 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 Scattering

P. Lobel, L. Blanc-Féraud, Ch. Pichot, and M. Barlaud

Inverse Problems, vol. 13, No. 12, pp. 403-410, Avril 1997.

The reconstruction of the complexe permittivity profile of inhomogeneous objects from measured scattered field data is a strongly nonlinear and ill-posed 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 edge-preserving 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 2-D Wavelet Transform Domain

L. Blanc-Féraud, P. Charbonnier, P. Lobel, and M. Barlaud

In International Conference on Acoustics, Speech and Signal Processing, volume V, pages 305--308, Adelaide, South Australia, April 1994.

Une nouvelle méthode en reconstruction tomographique utlisant une Transformée en Ondelettes 2-D (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 2-D est plus efficace que la TO 1-D.

[9] Different Spatial Iterative Methods For Microwave Inverse Scattering

P. Lobel, R. Kleinman, Ch. Pichot, L. Blanc-Féraud, 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 2D-TM objects using scattered near-field data in the microwave domain. For this comparative study, the first iterative algorithm is based on a Levenberg-Marquardt method which is a modified Gauss-Newton or Newton-Kantorovitch 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 Polak-Ribière conjugate gradient direction) were employed.

[10] Object reconstruction From Far-Field data Using Gradient and Gauss-Newton Type Methods

P. Lobel, R. Kleinman, Ch. Pichot, L. Blanc-Féraud, and M. Barlaud

In Digest USNC/URSI Radio Science Meeting, page 233, Newport Beach, California, USA, June 1995. Communication invitée.

The reconstruction of 2D-TM objects using measured scattered far-field data is presented in this paper. Two iterative methods have been used. The first one is based on a Levenberg-Marquardt 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 Tomography

P. Lobel, R. Kleinman, Ch. Pichot, L. Blanc-Féraud, 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 2D-TM case. The nature of this problem is strongly non-linear and ill posed when quantitative imaging is required. The algorithm presented here, based on a gradient method, is applied to the complete non-linear 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 Polak-Ribière 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 edge-preserving potential functions PHI.

[12] Conjugate Gradient Algorithm with Edge-Preserving Regularization for Microwave Inverse Scattering

P. Lobel, L. Blanc-Féraud, Ch. Pichot, and M. Barlaud

In Progress In Electromagnetics Research Symposium (PIERS'96), page 355, Innsbruck, Austria, 8-12 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 edge-preserving 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 Edge-Preserving Regularization for Image Reconstruction from Experimental Data

P. Lobel, Ch. Pichot, L. Blanc-Féraud, and M. Barlaud

In IEEE AP-S International Symposium, vol. 1, pp. 644--647, Baltimore, Maryland, USA, July 21th-26th, 1996. Communication invitée.

The reconstruction of the complex permittivity profile of 2D-TM objects using scattered far-field data is considered. In order to solve this nonlinear and ill-posed 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 Imaging

Ch. Pichot, P. Lobel, L. Blanc-Féraud, 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 Newton-Kantorovitch and conjugate gradient method. A standart Tikhonov regularization with identity and gradient operators and an edge-preserving regularization, using potential functions have been applied. In this last and nonlinear case, we make use of an algorithm based on a semi-quadratic regularization involving an explicit edge variable.

[19] Gauss-Newton and Gradient Methods for Microwave Tomography

Ch. 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 far-field scattered data in the 2D-TM case. Applications concerned here are medical imaging, nondestructive testing and target identification.

[22] Reconstruction Tomographique dans le Domaine de la Transformée en Ondelettes bidimensionnelle

P. Lobel, L. Blanc-Féraud, P. Charbonnier, and M. Barlaud

Research Note 93-60, 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 Edge-Preserving Regularization Method in Inverse Scattering

P. Lobel, L. Blanc-Féraud, Ch. Pichot, and M. Barlaud

Research Note 95-73, Laboratoire Informatique Signaux et Systèmes de Sophia Antipolis, December 1995.

This paper deals with the adaptation of an edge-preserving regularization method to the ill-posed 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 edge-preserving 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.