Caractérisation des performances minimales d’estimation pour des modèles d’observation non-standards

Chengfang Ren
Thesis defended on September 28, 2015, 2:00 PM at CentraleSupelec (Gif-sur-Yvette) Amphi Janet

In the parametric estimation context, estimators performances can be characterized, inter alia, by the mean square error and the resolution limit. The first quantifies the accuracy of estimated values and the second defines the ability of the estimator to allow a correct resolvability. This thesis deals first with the prediction the "optimal" MSE by using lower bounds in the hybrid estimation context (i.e. when the parameter vector contains both random and non-random parameters), second with the extension of Cramér-Rao bounds for non-standard estimation problems and finally to the characterization of estimators resolution. This thesis is then divided into three parts:

- First, we fill some lacks of hybrid lower bound on the MSE by using two existing Bayesian lower bounds: the Weiss-Weinstein bound and a particular form of Ziv-Zakai family lower bounds. We show that these extended lower bounds are tighter than the existing hybrid lower bounds in order to predict the optimal MSE.

- Second, we extend Cramer-Rao lower bounds for uncommon estimation contexts. Precisely: (i) Where the non-random parameters are subject to equality constraints (linear or nonlinear). (ii) For discrete-time filtering problems when the evolution of states is defined by a Markov chain. (iii) When the observation model differs to the real data distribution.

- Finally, we study the resolution of the estimators when their probability distributions are known. This approach is an extension of the work of Oh and Kashyap and the work of Clark to multi-dimensional parameters estimation problems.


Jury members :
M. Jean-Yves Tourneret  Professeur à l’INP-ENSEEIHT Toulouse  (Rapporteur)
M. Philippe Forster  Professeur à l’Université Paris-Ouest  (Rapporteur)
M. Cédric Richard  Professeur à l’Université Nice Sophia-Antipolis  (Examinateur)
M. Karim Abed-Meraim  Professeur à l’Université d’Orléans  (Examinateur)
M. Éric Chaumette  Professeur à l’ISAE  (Encadrant de thèse)
M. Jérôme Galy   Maître de conférences à l’Université de Montpellier  (Encadrant de thèse)
M. Alexandre Renaux  Maître de conférences à l’Université Paris-Sud  (Directeur de thèse)

Keywords: Parametric estimation, maximum likelihood estimator, maximum a posteriori estimator, performance analysis, hybrid estimation, lower bounds on the mean square error, statistical resolution limit.

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

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.


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

Développement de nouvelles méthodes itératives de reconstruction tomographique pour réduction des artefacts métalliques et réduction de la dose en imagerie dentaire

Long Chen
Thesis defended on February 05, 2015, 2:30 PM at CentraleSupelec (Gif-sur-Yvette) Salle des séminaires du L2S

This thesis contains two main themes: development of new iterative approaches for metal artifact reduction (MAR) and for dose reduction in dental CT (Computed Tomography). The metal artifacts are mainly from the beam-hardening, scatter and photon starvation in case of metal in contrast background like metallic dental implants in teeth. The first issue concerns about data correction on account of these effects. The second theme is contributed to reduce the radiation dose delivered to a patient by decreasing the number of the projections.

At first, for the purpose of the metal artifacts reduction, the polychromatic spectra of X-ray beam and scatter can be modeled by a non-linear direct modeling in the statistical methods. But the reconstruction by statistical methods is much time consuming. Consequently, we proposed an iterative algorithm with a linear direct modeling based on data correction (beam-hardening and scatter). We introduced a new beam-hardening correction without knowledge of the spectra of X-ray source and the linear attenuation coefficients of the materials and a new scatter estimation method based on the measurements as well.

Later, we continued to study the iterative approaches of dose reduction since the over-exposition or unnecessary exposition of irradiation during a scan has increased the patient's risk of radio-induced cancer. In practice, it may be interesting that one can reconstruct an object larger than the field of view of scanner. We proposed an iterative algorithm on super-short-scans on multiple scans in this case, which contain a minimal set of the projections for an optimal dose. Furthermore, we introduced a new scanning mode of variant angular sampling for reducing the number of projections on a single scan, which was adapted to the properties and predefined interesting regions of the scanned object. It needed fewer projections than the standard scanning mode of uniform angular sampling to reconstruct the objet correctly.

All of our approaches for MAR and dose reduction has been evaluated on real data. Thanks to our MAR methods, the quality of reconstructed images was improved notablely. Besides il did not introduce some new artifacts compared to the MAR methode of state of art NMAR [Meyer et al 2010]. We could reduce obviously the projection number with the proposed new scanning mode and schema of super-short-scans on multiple scans in particular case.

Membres du jury    
Directeur de thèse Mr RODET Thomas Professeur, ENS Cachan, SATIE
Co-encadrant Mr. GAC Nicolas Maître de conférences, Université Paris-Sud, L2S
Rapporteurs Mr. DESBAT Laurent Professeur des universités, Université Joseph Fourier
  Mr. BLEUET Pierre Ingénieur de recherche CEA, HDR
Examinateurs Mme NGUYEN-VERGER Maï Professeur des universités, Université de Cergy-Pontoise
  Mme MARCOS Sylvie Directeur de recherche, CNRS
Invitée Mme MAURY Colombe Ingénieur de recherche, Trophy, Carestream Dental