To overcome the ill-posedness of the inverse scattering problem, we introduce an appropriate way of representing the unknown permittivity profile which benefits from two a priori pieces of information which are commonly encountered. First, the unknown permittivity map has a limited spatial support which can be contained within a circular investigation area. Second, from physical reasoning based on the scattering operator, there is only a limited number of independent parameters that can be retrieved from the measured fields. Both pieces of a priori information can be adequately introduced by representing the unknown permittivity profile in terms of a Zernike polynomial expansion, correctly truncated according to the number of independent parameters. To investigate the effectiveness of such a Zernike representation, the reconstructions obtained from experimentally acquired data in the circular microwave scanner developed at the Institut Fresnel are analyzed.
International audienceThis article deals with the inverse scattering problem from scattered field data measured inside a closed microwave scanner. This system is presently being developed to demonstrate the potentiality of a non-invasive microwave imaging system for volumetric water content monitoring. The final goal is to retrieve soil moisture information as it is an important parameter for understanding fluid flow modelling, as well as water uptake by plants roots. Based on the actual state of the setup, we are proposing appropriate numerical tools, in particular a finite element formalism combined with a Lagrangian minimization scheme to provide a fast and accurate imaging tool. We will also show how we can improve the reconstruction algorithms by changing in a very simpler manner the measurement configuration, using either off-centred information or impedance boundary matching environment
International audienceA nonlinear inverse scattering problem is solved to retrieve the permittivity maps inside a microwave cylindrical scanner of circular cross-section. In this article, we show how we can improve this minimization scheme by taking advantage of several a priori pieces of information. In particular, a global representation based on a Zernike basis expansion is introduced in order to restrain the class of solutions to functions which have circular spatial support, as is the case with the encountered geometrical configuration. The level-set function formalism is also exploited as the targets are known to be homogeneous by parts. We will show how we can combine the spatial support information and the binary nature of the scatterer, with limited changes of the inversion algorithm. Both synthetic and experimental results will be presented in order to highlight the importance of combining all the pieces of available information
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