Thèse de doctorat en Électronique
Soutenue en 2009
à Paris 11 en cotutelle avec Malardalen University , dans le cadre de Ecole doctorale Sciences et Technologies de l'Information, des Télécommunications et des Systèmes (Orsay, Essonne) , en partenariat avec Université de Paris-Sud. Faculté des Sciences d'Orsay (Essonne) (autre partenaire) .
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This dissertation presents a contribution to quantitative microwave imaging for breast tumor detection. The study made in the frame of a joint supervision Ph. D. Thesis between University Paris-SUD 11 (France) and Mälardalen University (Sweden), has been conducted through two experimental microwave imaging setups, the existing 2. 45 GHz planar camera (France) and the multi-frequency flexible robotic system, (Sweden), under development. In this context a 2D scalar flexible numerical tool based on a Newton-Kantorovich (NK) scheme, has been developed. Quantitative microwave imaging is a three dimensional vectorial nonlinear inverse scattering problem, where the complex permittivity of an abject is reconstructed from the measured scattered field, produced by the object. The NK scheme is used in order to deal with the nonlinearity and the ill posed nature of this problem. A TM polarization and a two dimensional medium configuration have been considered in order to avoid its vectorial aspect. The solution is found iteratively by minimizing the square norm of the error with respect to the scattered field data. Consequently, the convergence of such iterative process requires, at least two conditions. First, an efficient calibration of the experimental system has to be associated to the minimization of model errors. Second, the mean square difference of the scattered field introduced by the presence of the tumor has to be large enough, according to the sensitivity of the imaging system. The existing planar camera associated to a flexible 2D scalar NK code, are considered as an experimental platform for quantitative breast imaging. A preliminary numerical study shows that the multi-view planar system is quite efficient for realistic breast tumor phantoms, according to its characteristics (frequency, planar geometry and water as a coupling medium), as long as realistic noisy data are considered. Furthermore, a multi-incidence planar system, more appropriate in term of antenna-array arrangement, is proposed and its concept is numerically validated. On the other hand, an experimental work which includes a new fluid-mixture for the realization of a narrow band cylindrical breast phantom, a deep investigation in the calibration process and model error minimization, are presented. This conducts to the first quantitative reconstruction of a realistic breast phantom by using the planar camera. Next, both the qualitative and quantitative reconstruction of 3D inclusions into the cylindrical breast phantom, by using data from all the retina, are shown and discussed. Finally, the extended work towards the flexible robotic system is presented.