Une approche bayésienne de l'inversion. Application à l'imagerie de diffraction dans les domaines micro-onde et optique

Abstract : In this work, we are interested in scattering imaging in 2D and 3D configurations, where our objective is to reconstruct an image (contrast function) of an unknown object using measurements of the scattered field that results from the interaction between the unknown object and a known incident field whose propagation direction and frequency can be varied. The difficulty of this problem lies in the non-linearity of the forward model and in the ill-posed nature of the inverse problem which requires the introduction of prior information (regularization). For this purpose, we use a Bayesian approach with a joint estimation of the object contrast, currents induced inside the objects and other model parameters. The forward continuous model is described by two coupled integral equations. The discrete counterparts of the latter are obtained by means of the method of moments (MoM). For the inversion, the Bayesian approach allows us to model our knowledge about the object in a probabilistic way. For the given applications, the object under test is known to be composed of a finite number of materials, which implies that the desired image consists of a finite number of compact homogeneous regions. This justifies the choice of a prior model based upon a mixture of Gaussian with a hidden Markovian variable that represents the label of the regions. The nonlinear nature of the forward model and the use of this prior leads to joint posterior estimators which are intractable. Therefore, an approximation of the posterior distribution is needed. Two approaches are possible : a numerical approach, for example MCMC, and an analytical approach as the variational Bayesian approach. We have tested both approaches and both of them yield very good reconstruction results compared to classical methods. However, the variational Bayesian approach allows a much faster reconstruction as compared to the MCMC stochastic sampling method.
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Signal and Image processing. Université Paris Sud - Paris XI, 2010. French


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Contributor : Hacheme Ayasso <>
Submitted on : Monday, February 7, 2011 - 5:48:10 PM
Last modification on : Friday, November 4, 2011 - 4:11:18 PM

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Hacheme Ayasso. Une approche bayésienne de l'inversion. Application à l'imagerie de diffraction dans les domaines micro-onde et optique. Signal and Image processing. Université Paris Sud - Paris XI, 2010. French. <tel-00564015>

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