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En imagerie nucléaire (scintigraphie, TEMP, TEP), les diagnostics sont fréquemment faits à l'aide des courbes d'activité temporelles des différents organes et tissus étudiés. Ces courbes représentent l'évolution de la distribution d'un traceur radioactif injecté dans le patient. Leur obtention est compliquée par la superposition des organes et des tissus dans les séquences d'images 2D, et il convient donc de séparer les différentes contributions présentes dans les pixels. Le problème de séparation de sources sous-jacent étant sous-déterminé, nous proposons d'y faire face dans cette thèse en exploitant différentes connaissances a priori d'ordre spatial et temporel sur les sources. Les principales connaissances intégrées ici sont les régions d'intérêt (ROI) des sources qui apportent des informations spatiales riches. Contrairement aux travaux antérieurs qui ont une approche binaire, nous intégrons cette connaissance de manière robuste à la méthode de séparation, afin que cette dernière ne soit pas sensible aux variations inter et intra-utilisateurs dans la sélection des ROI. La méthode de séparation générique proposée prend la forme d'une fonctionnelle à minimiser, constituée d'un terme d'attache aux données ainsi que de pénalisations et de relâchements de contraintes exprimant les connaissances a priori. L'étude sur des images de synthèse montrent les bons résultats de notre approche par rapport à l'état de l'art. Deux applications, l'une sur les reins, l'autre sur le cœur illustrent les résultats sur des données cliniques réelles. / In nuclear imaging (scintigraphy, SPECT, PET), diagnostics are often made with time activity curves (TAC) of organs and tissues. These TACs represent the dynamic evolution of tracer distribution inside patient's body. Extraction of TACs can be complicated by overlapping in the 2D image sequences, hence source separation methods must be used in order to extract TAC properly. However, the underlying separation problem is underdetermined. We propose to overcome this difficulty by adding some spatial and temporal prior knowledge about sources on the separation process. The main knowledge used in this work is region of interest (ROI) of organs and tissues. Unlike state of the art methods, ROI are integrated in a robust way in our method, in order to face user-dependancy in their selection. The proposed method is generic and minimize an objective function composed with a data fidelity criterion, penalizations and relaxations expressing prior knowledge. Results on synthetic datasets show the efficiency of the proposed method compare to state of the art methods. Two clinical applications on the kidney and on the heart are also adressed.

Les contours actifs sont parmi les méthodes de segmentation d'images les plus utilisées et de nombreuses implémentations ont vu le jour durant ces 25 dernières années. Parmi elles, l'approche greedy est considérée comme l'une des plus rapides et des plus stables. Toutefois, quelle que soit l'implémentation choisie, les résultats de segmentation souffrent grandement en présence d'occlusions, de concavités ou de déformation anormales de la forme. Si l'on dispose d'informations a priori sur la forme recherchée, alors son incorporation à un modèle existant peut permettre d'améliorer très nettement les résultats de segmentation. Dans cette thèse, l'inclusion de ce type de contraintes de formes dans un modèle de contour actif explicite est proposée. Afin de garantir une invariance à la rotation, à la translation et au changement d'échelle, les descripteurs de Fourier sont utilisés. Contrairement à la plupart des méthodes existantes, qui comparent la forme de référence et le contour actif en cours d'évolution dans le domaine d'origine par le biais d'une transformation inverse, la méthode proposée ici réalise cette comparaison dans l'espace des descripteurs. Cela assure à notre approche un faible temps de calcul et lui permet d'être indépendante du nombre de points de contrôle choisis pour le contour actif. En revanche, cela induit un biais dans la phase des coefficients de Fourier, handicapant l'invariance à la rotation. Ce problème est résolu par un algorithme original. Les expérimentations indiquent clairement que l'utilisation de ce type de contrainte de forme améliore significativement les résultats de segmentation du modèle de contour actif utilisé. / Active contours are widely used for image segmentation. There are many implementations of active contours. The greedy algorithm is being regarded as one of the fastest and stable implementations. No matter which implementation is being employed, the segmentation results suffer greatly in the presence of occlusion, context noise, concavities or abnormal deformation of shape. If some prior knowledge about the shape of the object is available, then its addition to an existing model can greatly improve the segmentation results. In this thesis inclusion of such shape constraints for explicit active contours is being implemented. These shape priors are introduced through the use of robust Fourier based descriptors which makes them invariant to the translation, scaling and rotation factors and enables the deformable model to converge towards the prior shape even in the presence of occlusion and contextual noise. Unlike most existing methods which compare the reference shape and evolving contour in the spatial domain by applying the inverse transforms, our proposed method realizes such comparisons entirely in the descriptor space. This not only decreases the computational time but also allows our method to be independent of the number of control points chosen for the description of the active contour. This formulation however, may introduce certain anomalies in the phase of the descriptors which affects the rotation invariance. This problem has been solved by an original algorithm. Experimental results clearly indicate that the inclusion of these shape priors significantly improved the segmentation results of the active contour model being used.

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We study a two-scale coupled system consisting of a macroscopic elliptic equation and a microscopic parabolic equation. This system models the interplay between a gas and liquid close to equilibrium within a porous medium with distributed microstructures. We use formal homogenization arguments to derive the target system. We start by proving well-posedness and inverse estimates for the two-scale system. We follow up by proposing a Galerkin scheme which is continuous in time and discrete in space, for which we obtain well-posedness, a priori error estimates and convergence rates. Finally, we propose a numerical error reduction strategy by refining the grid based on residual error estimators.

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Neste trabalho, apresentamos uma extensão da análise bayesiana objetiva feita em Fonseca et al. (2008), baseada nas distribuições a priori de Jeffreys para o modelo de regressão linear com erros t-Student, para os quais consideramos a suposição de heteoscedasticidade. Mostramos que a distribuição a posteriori dos parâmetros do modelo regressão gerada pela distribuição a priori é própria. Através de um estudo de simulação, avaliamos as propriedades frequentistas dos estimadores bayesianos e comparamos os resultados com outras distribuições a priori encontradas na literatura. Além disso, uma análise de diagnóstico baseada na medida de divergência Kullback-Leiber é desenvolvida com a finalidade de estudar a robustez das estimativas na presença de observações atípicas. Finalmente, um conjunto de dados reais é utilizado para o ajuste do modelo proposto. / In this work , we present an extension of the objective bayesian analysis made in Fonseca et al. (2008), based on Jeffreys priors for linear regression models with Student t errors, for which we consider the heteroscedasticity assumption. We show that the posterior distribution generated by the proposed Jeffreys prior, is proper. Through simulation study , we analyzed the frequentist properties of the bayesian estimators obtained. Then we tested the robustness of the model through disturbances in the response variable by comparing its performance with those obtained under another prior distributions proposed in the literature. Finally, a real data set is used to analyze the performance of the proposed model . We detected possible in uential points through the Kullback -Leibler divergence measure, and used the selection model criterias EAIC, EBIC, DIC and LPML in order to compare the models.

Submitted by Luciana Sebin (lusebin@ufscar.br) on 2016-09-26T18:57:40Z No. of bitstreams: 1 DissACRS.pdf: 1390452 bytes, checksum: a5365fdbf745228c0174f2643b3f7267 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-27T19:59:56Z (GMT) No. of bitstreams: 1 DissACRS.pdf: 1390452 bytes, checksum: a5365fdbf745228c0174f2643b3f7267 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-27T20:00:01Z (GMT) No. of bitstreams: 1 DissACRS.pdf: 1390452 bytes, checksum: a5365fdbf745228c0174f2643b3f7267 (MD5) / Made available in DSpace on 2016-09-27T20:00:08Z (GMT). No. of bitstreams: 1 DissACRS.pdf: 1390452 bytes, checksum: a5365fdbf745228c0174f2643b3f7267 (MD5) Previous issue date: 2016-02-18 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / In this work , we present an extension of the objective bayesian analysis made in Fonseca et al. (2008), based on Je reys priors for linear regression models with Student t errors, for which we consider the heteroscedasticity assumption. We show that the posterior distribution generated by the proposed Je reys prior, is proper. Through simulation study , we analyzed the frequentist properties of the bayesian estimators obtained. Then we tested the robustness of the model through disturbances in the response variable by comparing its performance with those obtained under another prior distributions proposed in the literature. Finally, a real data set is used to analyze the performance of the proposed model . We detected possible in uential points through the Kullback -Leibler divergence measure, and used the selection model criterias EAIC, EBIC, DIC and LPML in order to compare the models. / Neste trabalho, apresentamos uma extensão da análise bayesiana objetiva feita em Fonseca et al. (2008), baseada nas distribuicões a priori de Je reys para o modelo de regressão linear com erros t-Student, para os quais consideramos a suposicão de heteoscedasticidade. Mostramos que a distribuiçãoo a posteriori dos parâmetros do modelo regressão gerada pela distribuição a priori e própria. Através de um estudo de simulação, avaliamos as propriedades frequentistas dos estimadores bayesianos e comparamos os resultados com outras distribuições a priori encontradas na literatura. Além disso, uma análise de diagnóstico baseada na medida de divergência Kullback-Leiber e desenvolvida com analidade de estudar a robustez das estimativas na presença de observações atípicas. Finalmente, um conjunto de dados reais e utilizado para o ajuste do modelo proposto.

A Tomografia por Impedância Elétrica tem como objetivo estimar a distribuição de impedância elétrica dentro de uma região a partir de medidas de potencial elétrico coletadas apenas em seu contorno externo quando corrente elétrica é imposta neste mesmo contorno. Uma das aplicações para esta tecnologia é o monitoramento das condições pulmonares de pacientes em Unidades de Tratamento Intensivo. Dentre vários algoritmos, destacam-se os filtros de Kalman que abordam o problema de estimação sob o ponto de vista probabilístico, procurando encontrar a distribuição de probabilidade do estado condicionada à realização das medidas. Para que estes filtros possam ser utilizados, um modelo de evolução temporal do sistema sendo observado deve ser adotado. Esta tese propõe o uso de um modelo de evolução para a variação de volume de ar nos pulmões durante a respiração de um paciente sob ventilação artificial. Este modelo é utilizado no unscented Kalman filter, uma extensão não linear do filtro de Kalman. Tal modelo é ajustado em paralelo à estimação do estado, utilizando um esquema dual de estimação. Um algoritmo de segmentação de imagem é proposto para identificar as regiões pulmonares nas imagens estimadas e assim utilizar o modelo de evolução. Com o intuito de melhorar as estimativas, o método do erro de aproximação é utilizado no modelo de observação para mitigar os erros de modelagem e informação a priori é adicionada na solução do problema inverso mal-posto. O método é avaliado através de simulações numéricas e ensaio experimental coletado em um voluntário. Os resultados mostram que o método proposto melhora as estimativas feitas pelo filtro de Kalman, propiciando a visualização de imagens absolutas, dinâmicas e com bom nível de contraste entre os tecidos e órgãos internos. / Electrical impedance tomography estimates the electrical impedance distribution within a region given a set of electrical potential measurements acquired along its boundary at the same time that electrical currents are imposed on the same boundary. One of the applications of this technology is lung monitoring of patients in Intensive Care Units. One class of algorithms employed for the estimation are the Kalman filters which deal with the estimation problem in a probabilistic framework, looking for the probability density function of the state conditioned to the acquired measurements. In order to use such filters, an evolution models of the system must be employed. This thesis proposes an evolution model of the variation of air in the lungs of patients under artificial ventilation. This model is used on the Unscented Kalman Filter, a nonlinear extension of the Kalman filter. This model is adjusted in parallel to the state estimation, in a dual estimation scheme. An image segmentation algorithm is proposed for identifying the lungs in the images. In order to improve the estimate, the approximation error method is employed for mitigating the observation model errors and prior information is added for the solution of the ill-posed inverse problem. The method is evaluated with numerical simulations and with experimental data of a volunteer. The results show that the proposed method increases the quality of the estimates, allowing the visualization of absolute and dynamic images, with good level of contrast between the tissues and internal organs.

This paper is concerned with mesh refinement techniques for treating elliptic boundary value problems in domains with re- entrant edges and corners, and focuses on numerical experiments. After a section about the model problem and discretization strategies, their realization in the experimental code FEMPS3D is described. For two representative examples the numerically determined error norms are recorded, and various mesh refinement strategies are compared.