Séparation aveugle de sources : de l'instantané au convolutif

Fangchen FENG
Thesis defended on October 04, 2017, 3:30 PM at CentraleSupelec (Gif-sur-Yvette) Salle des séminaires du L2S

Composition du jury

M. Matthieu KOWALSKI   Université Paris-Sud     Directeur de these
M. Laurent GIRIN              Grenoble-INP, Gipsa-Lab  Rapporteur
M. Emmanuel VINCENT   Inria Grand-Est, Loria     Rapporteur
M. Roland BADEAU      Télécom ParisTech     Examinateur
M. Laurent DAUDET      Univ Paris-Diderot             Examinateur
M. Alexandre GRAMFORT   Inria Saclay, Neurospin     Examinateur 

Mots-clés :  Séparation aveugle de sources, Parcimonie, Représentation de Gabor, Factorisation en matrices nonnégatives, Problème inverse, Optimisation

Résumé : 
La séparation aveugle de source consiste à estimer les signaux de sources uniquement à partir des mélanges observés. Le problème peut être séparé en deux catégories en fonction du modèle de mélange: mélanges instantanés, où le retard et la réverbération (effet multi-chemin) ne sont pas pris en compte, et des mélanges convolutives qui sont plus généraux mais plus compliqués. De plus, le bruit additif au niveaux des capteurs et le réglage sous-déterminé, où il y a moins de capteurs que les sources, rendent le problème encore plus difficile. Dans cette thèse, tout d'abord, nous avons étudié le lien entre deux méthodes existantes pour les mélanges instantanés: analyse des composants indépendants (ICA) et analyse des composant parcimonieux (SCA). Nous avons ensuite proposé une nouveau formulation qui fonctionne dans les cas déterminés et sous-déterminés, avec et sans bruit. Les évaluations numériques montrent l'avantage des approches proposées. Deuxièmement, la formulation proposés est généralisés pour les mélanges convolutifs avec des signaux de parole. En intégrant un nouveau modèle d'approximation, les algorithmes proposés fonctionnent mieux que les méthodes existantes, en particulier dans des scénarios bruyant et / ou de forte réverbération. Ensuite, on prend en compte la technique de décomposition morphologique et l'utilisation de parcimonie structurée qui conduit à des algorithmes qui peuvent mieux exploiter les structures des signaux audio. De telles approches sont testées pour des mélanges convolutifs sous-déterminés dans un scénario non-aveugle. Enfin, en bénéficiant du modèle NMF (factorisation en matrice non-négative), nous avons combiné l'hypothèse de faible-rang et de parcimonie et proposé de nouvelles approches pour les mélanges convolutifs sous-déterminés. Les expériences illustrent la bonne performance des algorithmes proposés pour les signaux de musique, en particulier dans des scénarios de forte réverbération.

Modélisation électromagnétique et imagerie d'endommagements de laminés composites à renforcement de fibres Electromagnetic modeling and imaging of damages of fiber-reinforced composite laminates

Zicheng LIU
Thesis defended on October 03, 2017, 2:00 PM at CentraleSupelec (Gif-sur-Yvette) Salle du conseil du L2S - B4.40

Composition du jury proposé

M. Dominique LESSELIER        CNRS                               Directeur de thèse
Mme Amélie LITMAN                Université de Marseille     Rapportrice
M. Olivier DAZEL                      Université du Maine          Rapporteur
Mme Sonia FLISS                    ENSTA                               Examinatrice
M. Philippe LALANNE              CNRS                                Examinateur
M. Jean-Philippe GROBY        CNRS                                Examinateur
M. André NICOLET                  Université de Marseille     Examinateur
M. Edouard DEMALDENT       CEA LIST                          Invité
M. Yu ZHONG                         A*STAR Singapour            Invité

Mots-clés :  modélisation électromagnétique, imagerie électromagnétique, structure périodique

Résumé : 
On s'intéresse à la modélisation électromagnétique et à l'imagerie de stratifiés fibreux périodiques désorganisés. Les stratifiés ont des couches multiples et chaque couche est composée en incorporant périodiquement des fibres cylindriques dans une dalle homogène. Le matériau et la taille de la fibre peuvent changer de couche en couche, mais les périodes et les orientations sont obligées d'être identiques. Les fibres manquantes, déplacées, expansées, rétrécies et / ou circulaires détruisent la périodicité et les méthodes pour les structures périodiques deviennent inapplicables. La méthodologie Supercell fournit une structure périodique fictive, de sorte que la solution du champ partout dans l'espace peut être modélisée avec précision, à condition que la supercellule soit suffisamment grande. Cependant, l'efficacité de l'approche basée sur la supercellule n'est pas garantie en raison de la grande taille possible. Par conséquent, une approche alternative basée sur la théorie de l'équivalence est proposée, où les dommages sont équivalents à des sources dans les zones initialement intactes. Ensuite, le champ est une synthèse des réponses en raison de l'onde incidente et des sources équivalentes. Sur la base de la théorie de l'équivalence, l'emplacement des dommages se retrouve par recherche de sources équivalentes. Avec plusieurs sources et récepteurs en utilisation, quatre algorithmes de reconstruction, comprenant une solution moindres carrés, une solution "basic matching pursuit", MUSIC, et une approche itérative explorant la parcimonie conjointe de la solution désirée, permettent de récupérer les indices des fibres endommagées. Divers résultats numériques illustrent la disponibilité et la précision de l'approche de la modélisation et des performances d'imagerie haute résolution.

Contributions a l'analyse de données multivoie: algorithmes et applications

Olga Gisela LECHUGA LOPEZ
Thesis defended on July 03, 2017, 2:00 PM at CentraleSupelec (Gif-sur-Yvette) Amphi Blondel

Des méthodes statistiques telles que l'analyse discriminante, la régression logistique, la régression de Cox, et l'analyse canonique généralisée regularisée sont étendues au contexte des données multivoie, pour lesquelles, chaque individu est décrit par plusieurs instances de la même variable. Les données ont ainsi naturellement une structure tensorielle. Contrairement à leur formulation standard, une contrainte structurelle est imposée. L'intérêt de cette contrainte est double: d'une part elle permet une étude séparée de l'influence des variables et de l'influence des modalités, conduisant ainsi à une interprétation facilité des modèles. D'autre part, elle permet de restreindre le nombre de coefficients à estimer, et ainsi de limiter à la fois la complexité calculatoire et le phénomene de sur-apprentissage. Des stratégies pour gérer les problèmes liés au grande dimension des données sont également discutés. Ces différentes méthodes sont illustrées sur deux jeux de données réelles: (i) des données de spectroscopie et (ii) des données d'imagerie par résonance magnétique multi-modales pour prédire le rétablissement à long terme des patients après traumatisme cranien. Dans ces deux cas les méthodes proposées offrent de bons résultats en comparaison des résultats obtenus avec les approches standards.

Mots-clés :  Analyse de données, multiway, classification


Composition du jury proposé
M. Arthur TENENHAUS     CentraleSupélec   Directeur de thèse
M. Hervé ABDI     University of Texas   Rapporteur
M. Mohamed HANAFI     Université de Nantes   Rapporteur
M. Christophe AMBROISE     Université d'Evry   Examinateur
M. Robert SABATIER     Université de Montpellier   Examinateur
M. Remy BOYER     CentraleSupelec   Invité
M. Laurent LE BRUSQUET     CentraleSupelec   Invité

 

Performance and methods for sparse sampling : robustness to basis mismatch and kernel optimization.

Stéphanie BERNHARDT
Thesis defended on December 05, 2016, 2:00 PM at CentraleSupelec (Gif-sur-Yvette) Amphi F3-05

In this thesis, we are interested in two different low rate sampling schemes that challenge Shannon’s theory: the sampling of finite rate of innovation signals and compressed sensing.

Recently it has been shown that using appropriate sampling kernel, finite rate of innovation signals can be perfectly sampled even though they are non-bandlimited. In the presence of noise, reconstruction is achieved by a model-based estimation procedure. In this thesis, we consider the estimation of the amplitudes and delays of a finite stream of Dirac pulses using an arbitrary kernel and the estimation of a finite stream of arbitrary pulses using the Sum of Sincs (SoS) kernel. In both scenarios, we derive the Bayesian Cramér-Rao Bound (BCRB) for the parameters of interest. The SoS kernel is an interesting kernel since it is totally configurable by a vector of weights. In the first scenario, based on convex optimization tools, we propose a new kernel minimizing the BCRB on the delays, while in the second scenario we propose a family of kernels which maximizes the Bayesian Fisher Information, i.e., the total amount of information about each of the parameter in the measures. The advantage of the proposed family is that it can be user-adjusted to favor either of the estimated parameters.

Compressed sensing is a promising emerging domain which outperforms the classical limit of the Shannon sampling theory if the measurement vector can be approximated as the linear combination of few basis vectors extracted from a redundant dictionary matrix. Unfortunately, in realistic scenario, the knowledge of this basis or equivalently of the entire dictionary is often uncertain, i.e. corrupted by a Basis Mismatch (BM) error. The related estimation problem is based on the matching of continuous parameters of interest to a discretized parameter set over a regular grid. Generally, the parameters of interest do not lie in this grid and there exists an estimation error even at high Signal to Noise Ratio (SNR). This is the off-grid (OG) problem. The consequence of the BM and the OG mismatch problems is that the estimation accuracy in terms of Bayesian Mean Square Error (BMSE) of popular sparse-based estimators collapses even if the support is perfectly estimated and in the high Signal to Noise Ratio (SNR) regime. This saturation effect considerably limits the effective viability of these estimation schemes.

In this thesis, the BCRB is derived for CS model with unstructured BM and OG. We show that even though both problems share a very close formalism, they lead to different performances. In the biased dictionary based estimation context, we propose and study analytical expressions of the Bayesian Mean Square Error (BMSE) on the estimation of the grid error at high SNR. We also show that this class of estimators is efficient and thus reaches the Bayesian Cramér-Rao Bound (BCRB) at high SNR. The proposed results are illustrated in the context of line spectra analysis for several popular sparse estimator. We also study the Expected Cramér-Rao Bound (ECRB) on the estimation of the amplitude for a small OG error and show that it follows well the behavior of practical estimators in a wide SNR range.

In the context of BM and OG errors, we propose two new estimation schemes called Bias-Correction Estimator (BiCE) and Off-Grid Error Correction (OGEC) respectively and study their statistical properties in terms of theoretical bias and variances. Both estimators are essentially based on an oblique projection of the measurement vector and act as a post-processing estimation layer for any sparse-based estimator and mitigate considerably the BM (OG respectively) degradation. The proposed estimators are generic since they can be associated to any sparse-based estimator, fast, and have good statistical properties. To illustrate our results and propositions, they are applied in the challenging context of the compressive sampling of finite rate of innovation signals.

Keywords :

sparsity, basis mismatch, finite rate of innovation signals, kernel, sampling, Bayesian bounds

 Jury

M. Rémy BOYER Université Paris-Sud Directeur de thèse

Mme Sylvie MARCOS CNRS Co-Directeur de thèse

M. Pascal LARZABAL Université Paris-Sud Co-Encadrant de thèse

M. David BRIE Université de Lorraine Rapporteur

M. André FERRARI Université de Côte d'Azur Rapporteur

M. Eric CHAUMETTE ISAE-Supaéro Examinateur

M. Ali MOHAMMAD-DJAFARI CNRS Examinateur

M. Nicolas DOBIGEON Université de Toulouse Examinateur

A Bayesian approach for periodic components estimation for chronobiological signals

Mircea DUMITRU
Thesis defended on March 25, 2016, 10:00 AM at CentraleSupelec (Gif-sur-Yvette) Amphi Ampère

The toxicity and efficacy of more than 30 anticancer agents presents very high variations, depend-
ing on the dosing time. Therefore the biologists studying the circadian rhythm require a very precise
method for estimating the Periodic Components (PC) vector of chronobiological signals. Moreover,
in recent developments not only the dominant period or the PC vector present a crucial interest, but
also their stability or variability. In cancer treatment experiments the recorded signals corresponding
to different phases of treatment are short, from seven days for the synchronization segment to two or
three days for the after treatment segment. When studying the stability of the dominant period we have
to consider very short length signals relative to the prior knowledge of the dominant period, placed in
the circadian domain. The classical approaches, based on Fourier Transform (FT) methods are ineffi-
cient (i.e. lack of precision) considering the particularities of the data (i.e. the short length). Another
particularity of the signals considered in such experiments is the level of noise: such signals are very
noisy and establishing the periodic components that are associated with the biological phenomena and
distinguish them from the ones associated with the noise is a difficult task. In this thesis we propose
a new method for the estimation of the PC vector of biomedical signals, using the biological prior
informations and considering a model that accounts for the noise.

The experiments developed in the cancer treatment context are recording signals expressing a lim-
ited number of periods. This is a prior information that can be translated as the sparsity of the PC
vector. The proposed method considers the PC vector estimation as an Inverse Problem (IP) using
the general Bayesian inference in order to infer all the unknowns of our model, i.e. the PC vector
but also the hyperparameters. The sparsity prior information is modelled using a sparsity enforcing
prior law. In this thesis we propose a Student-t distribution, viewed as the marginal distribution of
a bivariate Normal - Inverse Gamma distribution. In fact, when the equality between the shape and
scale parameters corresponding to the Inverse Gamma distribution is not imposed, the marginal of the
Normal-Inverse Gamma distribution is a generalization of the Student-t distribution. We build a general
Infinite Gaussian Scale Mixture (IGSM) hierarchical model where we also assign prior distributions for
the hyperparameters. The expression of the joint posterior law of the unknown PC vector and the hy-
perparameters is obtained via the Bayes rule and then the unknowns are estimated via Joint Maximum
A Posteriori (JMAP) or Posterior Mean (PM). For the PM estimator, the expression of the posterior
distribution is approximated by a separable one, via Variational Bayesian Approximation (VBA), us-
ing the Kullback-Leibler (KL) divergence. Two possibilities are considered: an approximation with
partially separable distributions and an approximation with a fully separable one. The algorithms are
presented in detail and are compared with the ones corresponding to the Gaussian model. We examine
the practical convergency of the algorithms and give simulation results to compare their performances.
Finally we show simulation results on synthetic and real data in cancer treatment applications. The
real data considered in this thesis examines the rest-activity patterns and gene expressions of KI/KI
Per2::luc mouse, aged 10 weeks, singly housed in RT-BIO.

Keywords: Periodic Components (PC) vector estimation, Sparsity enforcing, Bayesian parameter
estimation, Variational Bayesian Approximation (VBA), Kullback-Leibler (KL) divergence, Infinite
Gaussian Scale Mixture (IGSM), Normal - Inverse Gamma, Inverse problem, Joint Maximum A Pos-
teriori (JMAP), Posterior Mean (PM), Chronobiology, Circadian rhythm, Cancer treatment.

Composition du jury

M. Ali MOHAMMAD-DJAFARI, Directeur de recherche CNRS, L2S, Gif-sur-Yvette, Directeur de thèse

M. Francis LÉVI, Professeur des Universités, University of Warwick, Angleterre, Co-directeur de thèse

M. Jean-François GIOVANELLI, Professeur des Universités, IMS, Bordeaux, Rapporteur

M. Ercan Engin KURUOGLU, Chercheur sénior CNRS, ISTI, Italie, Rapporteur

M. Alexandre RENAUX, Maître de conférences, Paris-Sud, Orsay, Examinateur

M. Michel KIEFFER, Professeur des Universités, Paris-Sud, Orsay, Examinateur

Panneaux complexes anisotropes et imagerie électromagnétique rapide.

Giacomo RODEGHIERO
Thesis defended on September 29, 2015, 2:00 PM at CentraleSupelec (Gif-sur-Yvette) Amphi Ampère

Non-Destructive Testing/Evaluation (NdT/E) of multi-layered composite materials for problems of quality, viability, safety and availability of systems involving manufactured parts (in aeronautics and in automotive industry, as a good example) has become an interesting and challenging task nowadays. The focus of the PhD thesis is on the electromagnetic (EM) imaging of complex anisotropic multi-slab composite panels as increasingly encountered in applications, yet source of strong challenges at modeling stage and even more at often-in-infancy imaging stage. From eddy-currents to microwaves, there is a strong need to make available modeling and imaging procedures that are robust, fast, accurate and useful to potential end-users' decision about potential defects both at low-frequency (LF) (conductive materials, carbon-fiber like) and high-frequency (HF) (dielectric materials, glass-fiber like). Moreover, it is important to get the results in close-to-real-time. However, this requires an accurate response to external sources of the multilayers, considering the layers which these composite structures are made of as undamaged or damaged. The modeling at forward stage is managed via a first-order solution involving the dyadic Green's functions (DGF) of the layers along with the depolarization tensor of the assumed defects when they are small enough vis-à-vis the skin depth (LF case) or the wavelength (HF case). The accuracy of the DGF has to be ensured even if the sources lie far away from the origin, which yields a fast-oscillating spectrum of the dyads. The Padua-Domínguez interpolation-integration technique is introduced herein in order to evaluate in an effective fashion fast-oscillating integrals.

Damages or disorders, which these composite structures may suffer from, are of many kinds. One could mention voids, fluid-filled cavities or uniaxial defects with obvious impacts on the electromagnetic and geometric parameters of the multilayers. That is, the task to make available to end-users imaging algorithms tailored to detect the presence of defects. The well-known standard MUltiple SIgnal Classification (MUSIC) algorithm, which is based on the Singular Value Decomposition (SVD) of such DGF, is here applied to localize the positions of small multiple defects with weak interaction embedded in anisotropic uniaxial media. The main drawback of MUSIC is its sensitivity with respect to the noise. Therefore, MUSIC with enhanced resolution and Recursively Applied and Projected (RAP) MUSIC are introduced to overcome such a drawback of the standard algorithm and to provide quality results with better resolution.

Jury :

H. Haddar, Directeur de recherche INRIA, DEFI-CMAP, Palaiseau, rapporteur,
A. Tamburrino, Professeur, Università degli Studi di Cassino e del Lazio Meridionale, Cassino, rapporteur,
M. Bonnet, Directeur de recherche CNRS, POems, Unité de Mathématiques Appliquées, Palaiseau, examinateur,
J.-P. Groby, Chargé de recherche CNRS, Laboratoire d'Acoustique de l'Université du Maine, Le Mans, examinateur,
C. Reboud, Ingénieur-chercheur, CEA LIST, Département Imagerie Simulation pour le Contrôle, Saclay, examinateur,
D. Lesselier, Directeur de recherche CNRS, L2S, Gif-sur-Yvette, Directeur de thèse.

 

Diffraction électromagnétique par des laminés plans renforcés par des fibres cylindriques arrangées périodiquement.

Changyou Li
Thesis defended on September 28, 2015, 2:00 PM at CentraleSupelec (Gif-sur-Yvette) Amphi Ampère

The contribution corresponds to the electromagnetic modeling of fiber-reinforced periodically organized composites. The final goal is to gain a good understanding of their electromagnetic behavior as well as to acquire images that should exhibit the location of possibly damaged zones, and provide some quantification of these zones. The thesis focuses on the scattering of well-organized periodic structures and building up an efficient full-wave computational model for multilayered composites, wherein each layer is reinforced by a periodic array of fibers, which is the first step for further study of the disorganized one.

The work firstly considered the scattering problem of a slab in which infinite circular fibers, with the same radius, are periodically embedded with the same orientation of their axes and the same center-to-center distance. A 2-dimensional problem with normally and obliquely incident E- and H-polarized plane waves as well as Gaussian beams is firstly considered for understanding the principles and philosophies of the used mode-matching method and multipole expansion. Then the work is extended to the investigation of the scattering of the slab to a conically incident 3-dimensional electromagnetic wave, which shows the potential of the work for obtaining the response of the structure to a point source.

A more practical but complicated multilayered composite, constructed by stacking up the slabs one over the other, is further investigated. Two different composites are taken into account. To study the first composite, with fibers in different layers having the same orientations, T-matrix- and S-matrix-based methods are introduced into the work for solving the linear system produced by mode-matching at the boundaries between two adjacent layers. Then, further investigation of the second kind of composite, wherein the fibers within different layers are orientated into different directions, is carried out by extending the approach properly.
Some attention is also given to homogenization issues, so as to link small-scale approaches as developed in the thesis with large-scale ones as often considered in non-destructive testing of composite laminates.

Extensive numerical simulations are proposed, validated with results existing in the literature (notably the ones of photonic crystals) and by using brute-force solvers. Emphasis is also on special cases of composites (glass-fiber- and graphite-fiber-based ones) as most often faced in practical applications, with appropriate frequency bands chosen in harmony with the dielectric or conductive aspect of the reinforcing fibers.

 

Composition du jury :

O. Dazel, Professeur, Université du Maine, Le Mans, rapporteur,
A. Nicolet, Professeur, Aix-Marseille Université, Marseille, rapporteur,
J.-J. Greffet, Professeur, Laboratoire Charles Fabry de l'Institut d'Optique, Palaiseau, examinateur,
P. Joly, Directeur de recherche INRIA, Palaiseau, examinateur,
C. Reboud, Ingénieur-chercheur, CEA LIST, Département Imagerie Simulation pour le Contrôle, Saclay, examinateur,
D. Lesselier, Directeur de recherche CNRS, L2S, Gif-sur-Yvette, Directeur de thèse.

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

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

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