Approches bayésiennes en tomographie micro-ondes. Application à l'imagerie du cancer du sein

Leila GHARSALLI
Thesis defended on April 10, 2015, 10:30 AM at CentraleSupelec (Gif-sur-Yvette) Amphi F3-05

This work concerns 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 denoted as ``the inverse problem'' as opposed to the associated forward problem that consists of 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. The latter is based upon 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 its 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 introduce prior knowledge appropriate to the sought object by considering that the latter is composed of a finite number of homogeneous materials distributed into compact and homogeneous regions. This information is introduced by means of a "Gauss-Markov-Potts" model. In addition, Bayesian computations yield the posterior distribution of all the unknowns from which we can define the point estimators. We proceed then to identify the posterior estimators via variational approximation methods and thereby to reconstruct images of the thought object.

The main contributions of this work are methodological and algorithmic. They are illustrated by an application of microwave tomography to breast cancer imaging. The latter is in itself a very important and original aspect of the thesis. Indeed, imaging of breast cancer using microwaves is a very interesting alternative to X-ray mammography, but it is still at an exploratory stage.

Members:

Directeur de thèse   Mr Duchêne Bernard  Chargé de recherche, CNRS
Co-directeur de thèse   Mr Mohammad-Djafari Ali   Directeur de recherche, CNRS
Encadrant   Mr Ayasso Hacheme  Maître de conférences à l'Université de Grenoble
Rapporteurs  Mme Litman Amélie  Maître de conférences à l'Université d'Aix-Marseille
                    Mr Massa Andréa  Professeur à l'Université de Trento, Italie
Examinateurs  Mme Blanc-Feraud Laure  Directrice de recherche, CNRS
                      Mr Pichot du Mezeray Christian  Directeur de recherche, CNRS