Approches bayésiennes en tomographie micro-ondes : applications à l'imagerie du cancer du sein

Abstract : This work concerns the problem of microwave tomography for application to biomedical imaging. The aim is to retreive both permittivity and conductivity of an unknown object from measurements of the scattered field that results from its interaction with a known interrogating wave. Such a problem is said to be inverse opposed to the associated forward problem that consists in calculating the scattered field while the interrogating wave and the object are known. The resolution of the inverse problem requires the prior construction of the associated forward model. This latter is based on an integral representation of the electric field resulting in two coupled integral equations whose discrete counterparts are obtained by means of the method of moments.Regarding the inverse problem, in addition to the fact that the physical equations involved in the forward modeling make it nonlinear, it is also mathematically ill-posed in the sense of Hadamard, which means that the conditions of existence, uniqueness and stability of the solution are not simultaneously guaranteed. Hence, solving this problem requires its prior regularization which usually involves the introduction of a priori information on the sought solution. This resolution is done here in a Bayesian probabilistic framework where we introduced a priori knowledge appropriate to the sought object by considering it to be composed of a finite number of homogeneous materials distributed in compact and homogeneous regions. This information is introduced through a "Gauss-Markov-Potts" model. In addition, the Bayesian computation gives the posterior distribution of all the unknowns, knowing the a priori and the object. We proceed then to identify the posterior estimators via variational approximation methods and thereby to reconstruct the image of the desired object.The main contributions of this work are methodological and algorithmic. They are illustrated by an application of microwave imaging to breast cancer detection. The latter is in itself a very important and original aspect of the thesis. Indeed, the detection of breast cancer using microwave imaging is a very interesting alternative to X-ray mammography, but it is still at an exploratory stage.
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Leila Gharsalli. Approches bayésiennes en tomographie micro-ondes : applications à l'imagerie du cancer du sein. Traitement du signal et de l'image [eess.SP]. Université Paris Sud - Paris XI, 2015. Français. ⟨NNT : 2015PA112048⟩. ⟨tel-01159537⟩

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