Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / A Tomografia de Processos é uma importante ferramenta para diversos setores da indústria. Tal importância vem da necessidade de obter informações sobre determinada propriedade física em regiões de complicado acesso, por exemplo, o interior de um duto. A tomografia é uma ferramenta muito versátil, podendo ser adaptada para investigar diversas propriedades físicas. Entre as diversas modalidades tomográficas está a elétrica, conhecida como Tomografia de Impedância Elétrica (EIT). A EIT pode ainda ser dividida em duas partes: Tomografia de Resistência Elétrica (ERT) e Tomografia de Capacitância Elétrica (ECT). Enquanto a ERT é capaz de distinguir materiais condutivos de não-condutivos, a ECT é capaz de diferenciar dois materiais não-condutivos pela sua permissividade elétrica. A modalidade de tomografia elétrica possui vantagens como: baixo tempo de aquisição, baixo custo e não-radioatividade. Os principais desafios enfrentados na tomografia elétrica são: a dependência da trajetória do campo em relação ao meio (efeito de campo mole) e a pouca quantidade de eletrodos disponı́veis para medições devido às dimensões dos mesmos. Em decorrência do efeito de campo mole, a soma da contribuição individual de cada pixel em uma região é diferente da contribuição real da região, em outras palavras, é um problema não-linear. Devido a pequena quantidade de eletrodos, em geral 8 ou 12, reconstruir uma imagem com resolução prática é um problema mal-posto. Muitos métodos foram propostos para contornar essas dificuldades, grande parte se baseia em um modelo linearizado do sistema e na resolução de um problema inverso. Neste trabalho é proposto um método de reconstrução de imagens com representação esparsa, no qual busca-se reconstruir uma imagem composta de poucos elementos de uma base redundante. Esses elementos são aprendidos a partir de sinais de treinamento e usados como entrada para um modelo de ECT. As respostas, em capacitância, desse modelo formam uma matriz de sensibilidade redundante. Tal matriz pode ser interpretada como uma linearização por partes do problema direto. Para validação desse algoritmo foram realizados experimentos em escoamentos bifásicos ar-água. Os sinais de treinamento foram obtidos com o uso de um sensor de ECT em conjunto com um sensor wire-mesh capacitivo. Os resultados obtidos demonstram a capacidade do método proposto em reconstruir imagens a partir de 8 medições de capacitâncias. As imagens reconstruı́das apresentam melhores resultados, segundo diferentes métricas, quando comparados a outros métodos com representações esparsas. / Process Tomography is an important tool for many sectors of industry. Such importance comes from the necessity of obtaining knowledge of physical properties from hard reaching places, as the interior of a solid object or pipe. Tomography is a very versatile tool, it can be adapted for investigating different physical properties. Among the many tomographic modalities is the electrical, know as Electrical Impedance Tomography (EIT). The EIT can also be divided in two: Electrical Resistance Tomography (ERT) and Electrical Capacitance Tomography (ECT). While the ERT is capable of distinguishing conducting materials from non-conducting ones, the ECT is capable of distinguishing two non-conducting materials by their electrical permittivity. The electrical modality has advantages such as: low acquisition time, low cost and non-radioactive. The main challenges of electrical tomography are: dependency of the trajectory of the field in the medium (effect know as soft-field) and the low number of electrodes available for measurement due to their sizes. As a result of the soft-field effect, the sum of individual contributions of small discrete segments in a given region is different from the contribution of the entire region as one. In other words, the relation between the electrical property and the electrical measurements are non-linear. Due to the small number of measuring electrodes, commonly 8 or 12, reconstructing images with practical resolution is an ill-posed problem. In order to overcome these obstacles, many methods were proposed and the majority are based on the resolution of an inverse problem of a linear model. This work proposes a method of image reconstruction with sparse inducing regularization that seeks to obtain an image representation with only few elements of a redundant basis. The elements of this basis are obtained from training images and used as input of an ECT simulation. The output capacitances of the model make up the columns of a redundant sensitivity matrix. Such matrix can be viewed as a piecewise linearization of the direct problem. For validation purposes, experimental tests were conducted on two-phase flows (air-water). The training signals were obtained from an experiment with a capacitive wire-mesh sensor along with an ECT sensor. The results obtained show that the proposed method is capable of reconstructing images from a set of only 8 capacitance measurements. The reconstructed images show better results, according to different metrics, when compared to other methods that also use sparse representations.

O ultrassom (US) é uma técnica bem consolidada que vem sendo amplamente utilizada para teste, caracterização e visualização de estruturas internas de materiais biológicos e não biológicos. Na Universidade Tecnológica Federal do Paraná, o grupo de pesquisa do US desenvolveu o sistema ULTRA-ORS que, apesar de adequado para pesquisa relacionada à excitação e recepção multicanal, possui tempo de computação muito elevado, devido a processamento em computador pessoal. Este trabalho apresenta a modelagem, implementação e validação de um sistema de processamento digital de sinais baseado em dispositivo FPGA (Field-Programmable Gate Array) de alto desempenho para reconstrução de imagens por US através da técnica beamforming. O software Simulink e a ferramenta DSP Builder foram empregados para simulação e transformação dos seguintes modelos em linguagem de descrição de hardware: filtro digital FIR (Finite Impulse Response), filtro de interpolação CIC (Cascaded Integrator-Comb), atraso variável, apodização, somatório coerente, decimação, demodulação com detecção de envoltória e compressão logarítmica. Após validação no Simulink, o projeto foi sintetizado para uma FPGA Stratix IV e implementado na placa Terasic DE4-230. A ferramenta SignalTap II do software Quartus II foi utilizada para aquisição dos sinais processados pela FPGA. Para avaliação gráfica e quantitativa da acurácia deste método, foram empregados dados brutos reais de US, adquiridos do ULTRA-ORS com frequência de amostragem de 40 MHz e resolução de 12 bits, e a função de custo da raiz quadrada do erro quadrático médio normalizado (NRMSE) em comparação com as mesmas funções implementadas através de scripts no Matlab. Como resultado principal do modelamento, além das respostas individuais de cada bloco implementado, são apresentadas as comparações entre as imagens reconstruídas pelo ULTRA-ORS e pelo processamento em FPGA para quatro janelas de apodização. A excelente concordância entre os resultados simulados e experimentais com valores de NRMSE inferiores à 6,2% e latência total de processamento de 0,83 µs corroboram a simplicidade, modularidade e efetividade do modelamento proposto para utilização em pesquisas sobre o processamento de sinais de US para reconstrução de imagens em tempo real. / Ultrasound (US) is a well-established technique that has been widely used for testing, characterizing and visualizing internal structures of biological and non-biological material. The US research group of the Federal University of Technology - Paraná developed the ULTRA-ORS system, which, although suitable for research related to multichannel excitation and reception, uses a large computing time, due to the personal computer processing. This research presents the modeling, implementation and validation of a digital processing system of signals based on a FPGA (Field-Programmable Gate Array) device of high performance for the reconstruction of images through US, using the beamforming technique. The software Simulink and the tool DSP Builder were used for simulation and transformation of the following models in hardware description language: digital filter FIR (Finite Impulse Response), CIC (Cascaded Integrator-Comb) Interpolation filter, variable delay, apodization, coherent summation, decimation, demodulation with envelope detection and logarithmic compression. After the Simulink validation, the design was synthesized for a Stratix IV FPGA and implemented on the Terasic DE4-230 board. The tool SignalTap II in the software Quartus II was used to acquire the processed signals from the FPGA. For the graphic and quantitative evaluation of the accuracy of this method, we used real raw US data, acquired from the ULTRA-ORS with sampling frequency of 40 MHz and 12-bit resolution, and the normalized root mean squared error (NRMSE) in comparison with the same functions implemented through scripts in Matlab. As a main result of the modeling, in addition to the individual responses of each implemented block, comparisons between the reconstructed images by ULTRA-ORS and FPGA processing for four apodization windows are presented. The excellent agreement between the simulated and experimental results with NRMSE values lower than 6.2% and total processing latency of 0.83 µs corroborates the simplicity, modularity and effectiveness of the proposed modeling for use in US signal processing research for real-time image reconstruction.

CNPq / Este trabalho tem por objetivo apresentar uma nova proposta aos algoritmos de Demosaicing existentes, utilizando uma abordagem mais flexível quanto ao uso do Color filter array (CFA) em imagens coloridas de único sensor. O algoritmo proposto tem como base a estrutura de problemas inversos, cujo funcionamento utiliza um modelo de operação matriz-vetor que é adaptável ao CFA empregado. A partir deste conceito, o algoritmo trata o problema de Demosaicing como o de minimização de função custo, com um termo referente à dependência da estimativa com os dados obtidos e com o modelo de captura, o outro termo é relacionado aos conhecimentos observados em imagens que podem ser explorados para uma estimativa mais precisa, tal elemento é chamado de Prior. A proposta estabelecida tem como base algoritmos de regularização com foco na alta correlação presente entre os canais de cor (R, G e B), e na suavidade local de regiões uniformes, essa base formaliza o Prior empregado no trabalho. A minimização da proposta é atingida iterativamente através do IRLS-CG, que é a combinação de dois algoritmos de minimização eficientes, que apresenta rápidas respostas, e a capacidade de trabalhar com a norma L1 em conjunto com a norma L2. Com o intuito de atestar a qualidade do algoritmo proposto, foi elaborado um experimento em que o mesmo foi testado com diferentes CFAs e em situação com ruído gaussiano de 35dB e sem ruído algum em imagens da base de dados da Kodak, e os resultados comparados com algoritmos do estado-da-arte, no qual o desempenho da proposta apresentou resultados excelentes, inclusive em CFAs que destoam do padrão Bayer, que é o mais comumente usado na atualidade. / This research presents a new proposal to Demosaicing algorithms, using a more flexible approach to deal with the Color filter array (CFA) in single sensor color imaging. The proposed algorithm is structured in the inverse problems model, whose functions employ a CFA adaptive matrix-vector operational model. From this concept, the Demosaicing problem is treated as a cost function minimization with two terms, one referring to the dependence between the estimation and the data provided by the acquisition model, and other term related to features observed in images, which can be explored to form a more precise estimation, this last term is known as Prior. The established proposal is applied in regularization algorithms with focus on the high correlation among color channels (R, G, and B), and in the local smoothness of uniform regions. Both characteristics organize the Prior employed in this work. The minimization proposed is iteratively achieved through IRLS-CG, which is the combination of two efficient minimization algorithms, that presents quick responses, and the capacity to deal with L1 and L2 norm at the same time. The quality of the proposed algorithm is verified in an experiment in which varous CFA were used and a situation with 35dB gaussian noise and another one with no noise applied to the Kodak dataset, and the results were compared with state-of-the-art algorithms, in which the performance of the proposed Prior showed excellent results, including when the CFA is different from Bayer’s, which is the most commonly used pattern.

O ultrassom (US) é uma técnica bem consolidada que vem sendo amplamente utilizada para teste, caracterização e visualização de estruturas internas de materiais biológicos e não biológicos. Na Universidade Tecnológica Federal do Paraná, o grupo de pesquisa do US desenvolveu o sistema ULTRA-ORS que, apesar de adequado para pesquisa relacionada à excitação e recepção multicanal, possui tempo de computação muito elevado, devido a processamento em computador pessoal. Este trabalho apresenta a modelagem, implementação e validação de um sistema de processamento digital de sinais baseado em dispositivo FPGA (Field-Programmable Gate Array) de alto desempenho para reconstrução de imagens por US através da técnica beamforming. O software Simulink e a ferramenta DSP Builder foram empregados para simulação e transformação dos seguintes modelos em linguagem de descrição de hardware: filtro digital FIR (Finite Impulse Response), filtro de interpolação CIC (Cascaded Integrator-Comb), atraso variável, apodização, somatório coerente, decimação, demodulação com detecção de envoltória e compressão logarítmica. Após validação no Simulink, o projeto foi sintetizado para uma FPGA Stratix IV e implementado na placa Terasic DE4-230. A ferramenta SignalTap II do software Quartus II foi utilizada para aquisição dos sinais processados pela FPGA. Para avaliação gráfica e quantitativa da acurácia deste método, foram empregados dados brutos reais de US, adquiridos do ULTRA-ORS com frequência de amostragem de 40 MHz e resolução de 12 bits, e a função de custo da raiz quadrada do erro quadrático médio normalizado (NRMSE) em comparação com as mesmas funções implementadas através de scripts no Matlab. Como resultado principal do modelamento, além das respostas individuais de cada bloco implementado, são apresentadas as comparações entre as imagens reconstruídas pelo ULTRA-ORS e pelo processamento em FPGA para quatro janelas de apodização. A excelente concordância entre os resultados simulados e experimentais com valores de NRMSE inferiores à 6,2% e latência total de processamento de 0,83 µs corroboram a simplicidade, modularidade e efetividade do modelamento proposto para utilização em pesquisas sobre o processamento de sinais de US para reconstrução de imagens em tempo real. / Ultrasound (US) is a well-established technique that has been widely used for testing, characterizing and visualizing internal structures of biological and non-biological material. The US research group of the Federal University of Technology - Paraná developed the ULTRA-ORS system, which, although suitable for research related to multichannel excitation and reception, uses a large computing time, due to the personal computer processing. This research presents the modeling, implementation and validation of a digital processing system of signals based on a FPGA (Field-Programmable Gate Array) device of high performance for the reconstruction of images through US, using the beamforming technique. The software Simulink and the tool DSP Builder were used for simulation and transformation of the following models in hardware description language: digital filter FIR (Finite Impulse Response), CIC (Cascaded Integrator-Comb) Interpolation filter, variable delay, apodization, coherent summation, decimation, demodulation with envelope detection and logarithmic compression. After the Simulink validation, the design was synthesized for a Stratix IV FPGA and implemented on the Terasic DE4-230 board. The tool SignalTap II in the software Quartus II was used to acquire the processed signals from the FPGA. For the graphic and quantitative evaluation of the accuracy of this method, we used real raw US data, acquired from the ULTRA-ORS with sampling frequency of 40 MHz and 12-bit resolution, and the normalized root mean squared error (NRMSE) in comparison with the same functions implemented through scripts in Matlab. As a main result of the modeling, in addition to the individual responses of each implemented block, comparisons between the reconstructed images by ULTRA-ORS and FPGA processing for four apodization windows are presented. The excellent agreement between the simulated and experimental results with NRMSE values lower than 6.2% and total processing latency of 0.83 µs corroborates the simplicity, modularity and effectiveness of the proposed modeling for use in US signal processing research for real-time image reconstruction.

CNPq / Este trabalho tem por objetivo apresentar uma nova proposta aos algoritmos de Demosaicing existentes, utilizando uma abordagem mais flexível quanto ao uso do Color filter array (CFA) em imagens coloridas de único sensor. O algoritmo proposto tem como base a estrutura de problemas inversos, cujo funcionamento utiliza um modelo de operação matriz-vetor que é adaptável ao CFA empregado. A partir deste conceito, o algoritmo trata o problema de Demosaicing como o de minimização de função custo, com um termo referente à dependência da estimativa com os dados obtidos e com o modelo de captura, o outro termo é relacionado aos conhecimentos observados em imagens que podem ser explorados para uma estimativa mais precisa, tal elemento é chamado de Prior. A proposta estabelecida tem como base algoritmos de regularização com foco na alta correlação presente entre os canais de cor (R, G e B), e na suavidade local de regiões uniformes, essa base formaliza o Prior empregado no trabalho. A minimização da proposta é atingida iterativamente através do IRLS-CG, que é a combinação de dois algoritmos de minimização eficientes, que apresenta rápidas respostas, e a capacidade de trabalhar com a norma L1 em conjunto com a norma L2. Com o intuito de atestar a qualidade do algoritmo proposto, foi elaborado um experimento em que o mesmo foi testado com diferentes CFAs e em situação com ruído gaussiano de 35dB e sem ruído algum em imagens da base de dados da Kodak, e os resultados comparados com algoritmos do estado-da-arte, no qual o desempenho da proposta apresentou resultados excelentes, inclusive em CFAs que destoam do padrão Bayer, que é o mais comumente usado na atualidade. / This research presents a new proposal to Demosaicing algorithms, using a more flexible approach to deal with the Color filter array (CFA) in single sensor color imaging. The proposed algorithm is structured in the inverse problems model, whose functions employ a CFA adaptive matrix-vector operational model. From this concept, the Demosaicing problem is treated as a cost function minimization with two terms, one referring to the dependence between the estimation and the data provided by the acquisition model, and other term related to features observed in images, which can be explored to form a more precise estimation, this last term is known as Prior. The established proposal is applied in regularization algorithms with focus on the high correlation among color channels (R, G, and B), and in the local smoothness of uniform regions. Both characteristics organize the Prior employed in this work. The minimization proposed is iteratively achieved through IRLS-CG, which is the combination of two efficient minimization algorithms, that presents quick responses, and the capacity to deal with L1 and L2 norm at the same time. The quality of the proposed algorithm is verified in an experiment in which varous CFA were used and a situation with 35dB gaussian noise and another one with no noise applied to the Kodak dataset, and the results were compared with state-of-the-art algorithms, in which the performance of the proposed Prior showed excellent results, including when the CFA is different from Bayer’s, which is the most commonly used pattern.

Les ostéocytes sont les plus nombreuses cellules du tissu osseux, enterrées dans la matrice osseuse. Elles sont interconnectées par des dendrites, situées dans des canaux appelés canalicules. Les lacunes ostéocytaires, les cavités dans lesquelles les cellules sont logées, avec les canalicules forment un réseau de communication à travers la matrice osseuse, permettant le transport des nutriments et des signaux. Ces cellules, considérées d’abord passives, ont révélé dernièrement leur rôle en tant que cellules mécanosensitives et orchestratrices du remodelage osseux. Malgré les progrès récents des techniques d'imagerie, aucune méthode disponible ne fournit une évaluation 3D adéquate du réseau lacuno-canaliculaire (LCN). Les objectifs de cette thèse ont porté sur l’imagerie 3D du LCN par tomographie synchrotron à rayons X (SR-CT), et le développement d’outils de détection et segmentation 3D de ce réseau cellulaire, afin de le quantifier et analyser. Nous démontrons la faisabilité de la SR-CT en géométrie parallèle pour imager le LCN dans le tissu osseux (voxel~300nm). Cette technique fournit des données 3D sur la morphologie du réseau cellulaire et aussi sur la composition de la matrice osseuse. Comparée aux méthodes d'imagerie 3D existantes, la SR-CT permet l'imagerie d’un volume de tissu beaucoup plus important, d'une manière plus simple et rapide. Cela rend possible l'étude de séries de spécimens afin d'obtenir des conclusions biomédicales. Nous proposons aussi l'utilisation de l’holotomographie divergente synchrotron, pour imager l'ultrastructure du tissu osseux (voxel~60nm). La reconstruction d'image fournit des cartes de phase, obtenues après application d'un algorithme d’inversion de phase adéquat. Cette technique a permis l'évaluation du réseau cellulaire avec une précision plus élevée et de visualiser, pour la première fois en 3D, l'organisation des fibres de collagène. Afin d'obtenir des résultats quantitatifs sur la géométrie du réseau cellulaire, celui doit être segmenté. À cause des limitations de la résolution spatiale, les canalicules apparaissent comme de structures tubulaires très fines (diamètre 1-3 voxels). Ceci, combiné avec le bruit, le faible contraste et la grande taille des images (8Go), rendent la segmentation difficile. Nous proposons une méthode de filtrage non-linéaire 3D, basée sur le rehaussement des structures linéaires, combiné avec un filtrage bilatéral. Cela permet une amélioration de la détection des canalicules, la réduction du bruit de fond et de la préservation des lacunes cellulaires. Pour la segmentation d'images, nous avons développé une méthode basée sur la croissance de région variationnelle. Nous proposons deux expressions de fonctionnelles d'énergie à minimiser, afin de détecter la structure souhaitée. Des résultats quantitatifs préliminaires sont obtenus à partir d’une analyse en composantes connexes sur des échantillons humaines et des observations relatives au réseau ostéocytaire sont présentés. / The osteocytes are the most abundant and longest living bone cells, embedded in the bone matrix. They are interconnected with each other through dendrites, located in slender canals called canaliculi. The osteocyte lacunae, cavities in which the cells are located, together with the canaliculi form a communication network throughout the bone matrix, permitting transport of nutrients, waste and signals. These cells were firstly considered passive, but lately it has become increasingly clear their role as mechanosensory cells and orchestrators of bone remodeling. Despite recent advances in imaging techniques, none of the available methods can provide an adequate 3D assessment of the lacuno-canalicular network (LCN). The aims of this thesis were to achieve 3D imaging of the LCN with synchrotron radiation X-ray computed tomography (SR-CT) and to develop tools for 3D detection and segmentation of this cell network, leading towards automatic quantification of this structure. We demonstrate the feasibility of parallel beam SR-CT to image in 3D the LCN (voxel~300 nm). This technique can provide data on both the morphology of the cell network and the composition of the bone matrix. Compared to the other 3D imaging methods, this enables imaging of tissue covering a number of cell lacunae three orders of magnitude greater, in a simpler and faster way. This makes possible the study of sets of specimens in order to reach biomedical conclusions. Furthermore, we propose the use of divergent holotomography, to image the ultrastructure of bone tissue (voxel~60 nm). The image reconstruction provides phase maps, obtained after the application of a suitable phase retrieval algorithm. This technique permits assessment of the cell network with higher accuracy and it enables the 3D organization of collagen fibres organization in the bone matrix, to be visualized for the first time. In order to obtain quantitative parameters on the geometry of the cell network, this has to be segmented. Due to the limitations in spatial resolution, canaliculi appear as 3D tube-like structures measuring only 1-3 voxels in diameter. This, combined with the noise, the low contrast and the large size of each image (8 GB), makes the segmentation a difficult task. We propose an image enhancement method, based on a 3D line filter combined with bilateral filtering. This enables improvement in canaliculi detection, reduction of the background noise and cell lacunae preservation. For the image segmentation we developed a method based on variational region growing. We propose two expressions for energy functionals to minimize in order to detect the desired structure, based on the 3D line filter map and the original image. Preliminary quantitative results on human femoral samples are obtained based on connected components analysis and a few observations related to the bone cell network and its relation with the bone matrix are presented.

Ce travail de thèse porte sur la reconstruction et la description des fonctions de distribution d'orientation (ODF) en imagerie de diffusion à haute résolution angulaire (HARDI) telle que l’imagerie par q-ball (QBI). Dans ce domaine, la fonction de distribution d’orientation (ODF) en QBI est largement utilisée pour étudier le problème de configuration complexe des fibres. Toutefois, jusqu’à présent, l’évaluation des caractéristiques ou de la qualité des ODFs reste essentiellement visuelle et qualitative, bien que l’utilisation de quelques mesures objectives de qualité ait également été reportée dans la littérature, qui sont directement empruntées de la théorie classique de traitement du signal et de l’image. En même temps, l’utilisation appropriée de ces mesures pour la classification des configurations des fibres reste toujours un problème. D'autre part, le QBI a souvent besoin d'un nombre important d’acquisitions pour calculer avec précision les ODFs. Ainsi, la réduction du temps d’acquisition des données QBI est un véritable défi. Dans ce contexte, nous avons abordé les problèmes de comment reconstruire des ODFs de haute qualité et évaluer leurs caractéristiques. Nous avons proposé un nouveau paradigme permettant de décrire les caractéristiques des ODFs de manière plus quantitative. Il consiste à regarder un ODF comme un nuage général de points tridimensionnels (3D), projeter ce nuage de points 3D sur un plan angle-distance (ADM), construire une matrice angle-distance (ADMAT), et calculer des caractéristiques morphologiques de l'ODF telles que le rapport de longueurs, la séparabilité et l'incertitude. En particulier, une nouvelle métrique, appelé PEAM (PEAnut Metric) et qui est basée sur le calcul de l'écart des ODFs par rapport à l’ODF (représenté par une forme arachide) d’une seule fibre, a été proposée et utilisée pour classifier des configurations intravoxel des fibres. Plusieurs méthodes de reconstruction des ODFs ont également été comparées en utilisant les paramètres proposés. Les résultats ont montré que les caractéristiques du nuage de points 3D peuvent être évaluées d'une manière relativement complète et quantitative. En ce qui concerne la reconstruction de l'ODF de haute qualité avec des données réduites, nous avons proposé deux méthodes. La première est basée sur une interpolation par triangulation de Delaunay et sur des contraintes imposées à la fois dans l’espace-q et dans l'espace spatial. La deuxième méthode combine l’échantillonnage aléatoire des directions de gradient de diffusion, le compressed sensing, l’augmentation de la densité de ré-échantillonnage, et la reconstruction des signaux de diffusion manquants. Les résultats ont montré que les approches de reconstruction des signaux de diffusion manquants proposées nous permettent d'obtenir des ODFs précis à partir d’un nombre relativement faible de signaux de diffusion. / This thesis concerns the reconstruction and description of orientation distribution functions (ODFs) in high angular resolution diffusion imaging (HARDI) such as q-ball imaging (QBI). QBI is used to analyze more accurately fiber structures (crossing, bending, fanning, etc.) in a voxel. In this field, the ODF reconstructed from QBI is widely used for resolving complex intravoxel fiber configuration problem. However, until now, the assessment of the characteristics or quality of ODFs remains mainly visual and qualitative, although the use of a few objective quality metrics is also reported that are directly borrowed from classical signal and image processing theory. At the same time, although some metrics such as generalized anisotropy (GA) and generalized fractional anisotropy (GFA) have been proposed for classifying intravoxel fiber configurations, the classification of the latters is still a problem. On the other hand, QBI often needs an important number of acquisitions (usually more than 60 directions) to compute accurately ODFs. So, reducing the quantity of QBI data (i.e. shortening acquisition time) while maintaining ODF quality is a real challenge. In this context, we have addressed the problems of how to reconstruct high-quality ODFs and assess their characteristics. We have proposed a new paradigm allowing describing the characteristics of ODFs more quantitatively. It consists of regarding an ODF as a general three-dimensional (3D) point cloud, projecting a 3D point cloud onto an angle-distance map (ADM), constructing an angle-distance matrix (ADMAT), and calculating morphological characteristics of the ODF such as length ratio, separability and uncertainty. In particular, a new metric, called PEAM (PEAnut Metric), which is based on computing the deviation of ODFs from a single fiber ODF represented by a peanut, was proposed and used to classify intravoxel fiber configurations. Several ODF reconstruction methods have also been compared using the proposed metrics. The results showed that the characteristics of 3D point clouds can be well assessed in a relatively complete and quantitative manner. Concerning the reconstruction of high-quality ODFs with reduced data, we have proposed two methods. The first method is based on interpolation by Delaunay triangulation and imposing constraints in both q-space and spatial space. The second method combines random gradient diffusion direction sampling, compressed sensing, resampling density increasing, and missing diffusion signal recovering. The results showed that the proposed missing diffusion signal recovering approaches enable us to obtain accurate ODFs with relatively fewer number of diffusion signals.

L'hadronthérapie est une méthode de traitement du cancer qui emploie des ions (carbone ou proton) au lieu des rayons X. Les interactions entre le faisceau et le patient produisent des radiations secondaires. Il existe une corrélation entre la position d'émission de certaines de ces particules et la position du pic de Bragg. Parmi ces particules, des gamma-prompt sont produits par les fragments nucléaires excités et des travaux actuels ont pour but de concevoir des systèmes de tomographie par émission mono-photonique capable d'imager la position d'émission ces radiations en temps réel, avec une précision millimétrique, malgré le faible nombre de données acquises. Bien que ce ne soit pas actuellement possible, le but in fine est de surveiller le dépôt de dose. La caméra Compton est un des système TEMP qui a été proposé pour imager ce type de particules, car elle offre une meilleure résolution énergétique et la possibilité d'avoir une image 3D. Cependant, en pratique l'acquisition est affectée par le bruit provenant d'autres particules secondaires, et les algorithmes de reconstruction des images Compton sont plus compliqués et encore peu aboutis, mais sur une bonne voie de développement. Dans le cadre de cette thèse, nous avons développé une chaîne complète allant de la simulation de l'irradiation d'un fantôme par un faisceau de protons allant jusqu'à la reconstruction tomographique des images obtenues à partir de données acquises par la caméra Compton. Nous avons étudié différentes méthodes de reconstruction analytiques et itératives, et nous avons développé une méthode de reconstruction itérative capable de prendre en compte les incertitudes de mesure sur l'énergie. Enfin nous avons développé des méthodes pour la détection de la fin du parcours des distributions gamma-prompt reconstruites. / Hadrontherapy is a cancer treatment method which uses ions (proton or carbon) instead of X-rays. Interactions between the beam and the patient produce secondary radiation. It has been shown that there is a correlation between the emission position of some of these particles and the Bragg peak position. Among these particles, prompt-gamma are produced by excited nuclear fragments and current work aims to design SPECT systems able to image the emission position the radiation in real time, with a millimetric precision, despite the low data statistic. Although it is not currently possible, the goal is to monitor the deposited dose. The Compton camera is a SPECT system that proposed for imaging such particles, because it offers a good energy resolution and the possibility of a 3D imaging. However, in practice the acquisition is affected by noise from other secondary particles and the reconstruction algorithms are more complex and not totally completed, but the developments are well advanced. In this thesis, we developed a complete process from the simulation of irradiation of a phantom by a proton beam up to the tomographic reconstruction of images obtained from data acquired by the Compton camera. We studied different reconstruction methods (analytical and iterative), and we have developed an iterative method able to consider the measurement uncertainties on energy. Finally we developed methods to detect the end-of-range of the reconstructed prompt-gamma distributions.

Electrical Impedance Tomography (EIT) is a non linear inverse problem in which the electrical conductivity or resistivity distribution across a closed domain of interest is reconstructed from the surface potentials measured at the domain boundary by injecting a constant sinusoidal current through an array of surface electrodes. Being a non-invasive, non-radiating, non-ionizing, portable and inexpensive methodology, EIT has been extensively studied in medical diagnosis, biomedical engineering, biotechnology, chemical engineering, industrial and process engineering, civil and material engineering, soil and rock science, electronic industry, defense field, nano-technology and many other fields of applied physics. The reconstructed image quality in EIT depends mainly on the boundary data quality and the performance of the reconstruction algorithm used. The boundary data accuracy depends on the design of the practical phantoms, current injection method and boundary data measurement process and precision. On the other hand, the reconstruction algorithm performance is highly influenced by the mathematical modeling of the system, performance of the forward solver and Jacobian computation, inverse solver and the regularization techniques. Hence, for improving the EIT system performance, it is essential to improve the design of practical phantom, instrumentation and image reconstruction algorithm. As the electrical impedance of biological materials is a function of tissue composition and the frequency of applied ac signal, the better assessment of impedance distribution of biological tissues needs multifrequency EIT imaging. In medical EIT, to obtain a better image quality for a complex organ or a body part, accurate domain modelling with a large 3D finite element mesh is preferred and hence, the computation speed becomes very expensive and time consuming. But, the high speed reconstruction with improved image quality at low cost is always preferred in medical EIT. In this direction, a complete multifrequency multifunction EIT (MfMf-EIT) system is developed and multifrequency impedance reconstruction is studied to improve the bioimpedance imaging. The MfMf-EIT system consists of an MfMf-EIT instrumentation (MfMf-EITI), high speed impedance image reconstruction algorithms (IIRA), a Personal Computer (PC) and a number of practical phantoms with EIT sensors or electrodes. MfMf-EIT system and high speed IIRA are studied tested and evaluated with the practical phantoms and the multifrequency impedance imaging is improved with better image quality as well as fast image reconstruction. The MfMf-EIT system is also applied to the human subjects and the impedance imaging is studied for human body imaging and the system is evaluated. MfMf-EIT instrumentation (MfMf-EITI) consists of a multifrequency multifunction constant current injector (MfMf-CCI), multifrequency multifunction data acquisition system (MfMf DAS), a programmable electrode switching module (P-ESM) and a modified signal conditioner blocks (M-SCB) or data processing unit (DPU). MfMf-CCI, MfMf-DAS, P-ESM and M-SCBs are interfaced with a LabVIEW based data acquisition program (LV-DAP) controlled by a LabVIEW based graphical user interface (LV-GUI). LV-GUI controls the current injection and data acquisition with a user friendly, fast, reliable, efficient measurement process. The data acquisition system performance is improved by the high resolution NIDAQ card providing high precision measurement and high signal to noise ratio (SNR). MfMf-EIT system is developed as a versatile data acquisition system with a lot of flexibilities in EIT parameter selection that allows studying the image reconstruction more effectively. MfMf-EIT instrumentation controls the multifrequency and multifunctioned EIT experimentation with a number of system variables such as signal frequency, current amplitude, current signal wave forms and current injection patterns. It also works with either grounded load CCI or floating load CCI and collects the boundary data either in grounded potential form or differential form. The MfMf-EITI is futher modified to a battery based MfMf-EIT (BbMfMf-EIT) system to obtain a better patient safety and also to improve the SNR of the boundary data. MfMf-EIT system is having a facility of injecting voltage signal to the objects under test for conducting the applied potential tomography (APT). All the electronic circuit blocks in MfMf-EIT instrumentation are tested, evaluated and calibrated. The frequency response, load response, Fast Fourier Transform (FFT) studies and DSO analysis are conducted for studying the electronic performance and the signal quality of all the circuit blocks. They are all evaluated with both the transformer based power supply (TBPS) and battery based power supply (BBPS). MfMf-DAS, P-ESM and LV-DAP are tested and evaluated with digital data testing module (DDTM) and practical phantoms. A MatLAB-based Virtual Phantom for 2D EIT (MatVP2DEIT) is developed to generate accurate 2D boundary data for assessing the 2D EIT inverse solvers and its image reconstruction accuracy. It is a MATLAB-based computer program which defines a phantom domain and its inhomogeneities to generate the boundary potential data by changing its geometric parameters. In MatVP2DEIT, the phantom diameter, domain discretization, inhomogeneity number, inhomogeneity geometry (shape, size and position), electrode geometry, applied current magnitude, current injection pattern, background medium conductivity, inhomogeneity conductivity all are set as the phantom variables and are chosen indipendently for simulating different phantom configurations. A constant current injection is simulated at the phantom boundary with different current injection protocols and boundary potential data are calculated. A number of boundary data sets are generated with different phantom configurations and the resistivity images are reconstructed using EIDORS (Electrical Impedance Tomography and Diffuse Optical Tomography Reconstruction Software). Resistivity images are evaluated with the resistivity parameters and contrast parameters estimated from the elemental resistivity profiles of the reconstructed impedance images. MfMf-EIT system is studied, tested, evaluated with a number of practical phantoms eveloped with non-biological and biological materials and the multifrequency impedance imaging is improved. A number of saline phantoms with single and multiple inhomogeneities are developed and the boundary data profiles are studied and the phantom geometry is modified. NaCl-insulator phantoms and the NaCl-vegetable phantoms with different inhomogeneity configurations are developed and the multifrequency EIT reconstruction is studied with different current patterns, different current amplitudes and different frequencies using EIDORS as well as the developed IIRAs developed in MATLAB to evaluate the phantoms and MfMf-EIT system. Real tissue phantoms are developed with different chicken tissue backgrounds and high resistive inhomogeneities and the resistivity image reconstruction is studied using MfMf-EIT system. Chicken tissue phantoms are developed with chicken muscle tissue (CMTP) paste or chicken tissue blocks (CMTB) as the background mediums and chicken fat tissue, chicken bone, air hole and nylon cylinders are used as the inhomogeneity to obtained different phantom configurations. Resistivity imaging of all the real tissue phantoms is reconstructed in EIDORS and developed IIRAs with different current patterns, different frequencies and the images are evaluated by the image parameters to assess the phantoms as well as the MfMf-EIT system. Gold electrode phantoms are developed with thin film based flexible gold electrode arrays for improved bioimpedance and biomedical imaging. The thin film based gold electrode arrays of high geometric precision are developed on flexible FR4 sheet using electro-deposition process and used as the EIT sensors. The NaCl phantoms and real tissue phantoms are developed with gold electrode arrays and studied with MfMf-EIT system and and the resiulsts are compared with identical stainless steel electrode phantoms. NaCl phantoms are developed with 0.9% NaCl solution with single and multiple insulator or vegetable tissues as inhomogeneity. Gold electrode real tissue phantoms are also developed with chicken muscle tissues and fat tissues or other high resistive objects. The EIT images are reconstructed for the gold electrode NaCl phantoms and the gold electrode real tissue phantoms with different phantom geometries, different inhomogeneity configurations and different current patterns and the results are compared with identical SS electrode phantoms. High speed IIRAs called High Speed Model Based Iterative Image Reconstruction (HSMoBIIR) algorithms are developed in MATLAB for impedance image reconstruction in Electrical Impedance Tomography (EIT) by implementing high speed Jacobian calculation techniques using “Broyden’s Method (BM)” and “Adjoint Broyden’s Method (ABM)”. Gauss Newton method based EIT inverse solvers repeatitively evaluate the Jacobian (J) which consumes a lot of computation time for reconstruction, whereas, the HSMoBIIR with Broyden’s Methods (BM)-based accelerated Jacobian Matrix Calculators (JMCs) provides the high speed schemes for Jacobian (J) computation which is integrated with conjugate gradient scheme (CGS) for fast impedance reconstruction. The Broyden’s method based HSMoBIIR (BM-HSMoBIIR) and Adjoint Broyden’s method based HSMoBIIR (ABM-HSMoBIIR) algorithm are developed for high speed improved impedance imaging using BM based JMC (BM-JMC) and ABM-based JMC (ABM-JMC) respectively. Broyden’s Method based HSMoBIIR algorithms make explicit use of secant and adjoint information that can be obtained from the forward solution of the EIT governing equation and hence both the BM-HSMoBIIR and ABM-HSMoBIIR algorithms reduce the computational time remarkably by approximating the system Jacobian (J) successively through low-rank updates. The impedance image reconstruction is studied with BM-HSMoBIIR and ABM-HSMoBIIR algorithms using the simulated and practical phantom data and results are compared with a Gauss-Newton method based MoBIIR (GNMoBIIR) algorithm. The GNMoBIIR algorithm is developed with a Finite Element Method (FEM) based flexible forward solver (FFS) and Gauss-Newton method based inverse solver (GNIS) working with a modified Newton-Raphson iterative technique (NRIT). FFS solves the forward problem (FP) to obtain the computer estimated boundary potential data (Vc) data and NRIT based GNIS solve the inverse problem (IP) and the conductivity update vector [Δσ] is calculated by conjugate gradient search by comparing Vc measured boundary potential data (Vm) and using the Jacobian (J) matrix computed by the adjoint method. The conductivity reconstruction is studied with GNMoBIIR, BM-HSMoBIIR and ABM-HSMoBIIR algorithms using simulated data a practical phantom data and the results are compared. The reconstruction time, projection error norm (EV) and the solution error norm (Eσ) produced in HSMoBIIR algorithms are calculated and compared with GNMoBIIR algorithm. Results show that both the BM-HSMoBIIR and ABM-HSMoBIIR algorithms successfully reconstructs the conductivity distribution of the domain under test with its proper inhomogeneity and background conductivities for simulation as well as experimental studies. Simulated and practical phantom studies demonstrate that both the BM-HSMoBIIR and ABM-HSMoBIIR algorithms accelerate the impedance reconstruction by more than five times. It is also observed that EV and Eσ are reduced in both the HSMoBIIR algorithms and hence the image quality is improved. Noise analysis and convergence studies show that both the BM-HSMoBIIR and ABM-HSMoBIIR algorithms works faster and better in noisy conditions compared to GNMoBIIR. In low noise conditions, BM-HSMoBIIR is faster than to ABM-HSMoBIIR algorithm. But, in higher noisy environment, the ABM-HSMoBIIR is found faster and better than BM-HSMoBIIR. Two novel regularization methods called Projection Error Propagation-based Regularization (PEPR) and Block Matrix based Multiple Regularization (BMMR) are proposed to improve the image quality in Electrical Impedance Tomography (EIT). PEPR method defines the regularization parameter as a function of the projection error contributed by the mismatch (difference) between the data obtained from the experimental measurements (Vm) and calculated data (Vc). The regularization parameter in the reconstruction algorithm gets modified automatically according to the noise level in measured data and ill-posedness of the Hessian matrix. The L-2 norm of the projection error is calculated using the voltage difference and it is used to find the regularization parameter in each iteration in the reconstruction algorithm. In BMMR method, the response matrix (JTJ) obtained from the Jacobian matrix (J) has been partitioned into several sub-block matrices and the highest eigenvalue of each sub-block matrices has been chosen as regularization parameter for the nodes contained by that sub-block. The BMMR method preserved the local physiological information through the multiple regularization process which is then integrated to the ill-posed inverse problem to make the regularization more effective and optimum for all over the domain. Impedance imaging with simulated data and the practical phantom data is studied with PEPR and BMMR techniques in GNMoBIIR and EIDORS and the reconstructed images are compared with the single step regularization (STR) and Modified Levenberg Regularization (LMR). The projection error and the solution error norms are estimated in the reconstructions processes with PEPR and the BMMR methods and the results are compared with the errors estimated in STR and modified LMR techniques. Reconstructed images obtained with PEPR and BMMR are also studied with image parameters and contrast parameters and the reconstruction performance with PEPR and BMMR are evaluated by comparing the results with STR and modified LMR. PEPR and BMMR techniques are successfully implemented in the GNMoBIIR and EIDORS algorithms to improve the impedance image reconstruction by regularizing the solution domain in EIT reconstruction process. As the multifrequency EIT is always preferred in biological object imaging for better assessments of the frequency dependent bioimpedance response, multifrequency impedance imaging is studied with MfMf-EIT system developed for biomedical applications. MfMf-EIT system is studied, tested and evaluated with practical phantoms suitably developed for multifrequency impedance imaging within a wide range of frequency. Different biological materials are studied with electrical impedance spectroscopy (EIS) and a number of practical biological phantoms suitable for multifrequency EIT imaging are developed. The MfMf-EIT system is studied, tested and evaluated at different frequency levels with different current patterns using a number of NaCl phantoms with single, multiple and hybrid vegetable tissue phantoms as well as with chicken tissue phantoms. BbMfMf-EIT system is also studied and evaluated with the multifrequency EIT imaging using the developed biological phantoms. The developed MfMf-EIT system is applied on human body for impedance imaging of human anatomy. Impedance imaging of human leg and thigh is studied to visualize the muscle and bone tissues using different current patterns and different relative electrode positions. Ag/AgCl electrodes are attached to the leg and thigh using ECG gel and the boundary data are collected with MfMf-EIT EIT system by injecting a 1 mA and 50 kHz sinusoidal constant current with neighbouring and opposite current injection patterns. Impedance images of the femur bone of the human thigh and the tibia and fibula bones of the human leg along with the muscle tissue backgrounds are reconstructed in EIDORS and GNMoBIIR algorithms. Reconstructed resistivity profiles of bone and muscles are compared with the resistivity data profiles reported in the published literature. Impedance imaging of leg and thigh is studied with MfMf-EIT system for different current patterns, relative electrode positions and the images are evaluated to assess the system reliability. Battery based MfMf-EIT system (BbMfMf-EIT) is also studied for human leg and thigh imaging and it is observed that MfMf-EIT system and BbMfMf-EIT system are suitable for impedance imaging of human body imaging though the BbMfMf-EIT system increases the patiet safety. Therefore, the developed MfMf-EIT and BbMfMf-EIT systems are found quite suitable to improve the bio-impedance imaging in medical, biomedical and clinical applications as well as to study the anatomical and physiological status of the human body to diagnose, detect and monitor the tumors, lesions and a number of diseases or anatomical abnormalities in human subjects.

Ce travail de thèse, inclus dans un projet structurant plus vaste, projet SIMOVI (SImulation des MOuvements du VIsage), s’attache à étudier spécifiquement la mimique faciale en corrélant les déplacements visibles du revêtement cutané et les mouvements musculaires internes à travers le développement de plusieurs méthodologies. L’ensemble de la mimique faciale ne pouvant être étudié, étant donné la multitude d’expressions, les mouvements pertinents à étudier dans nos travaux ont été identifiés. Ces mouvements ont été caractérisés chez 23 sujets jeunes dans une analyse descriptive qualitative et clinique, basée sur une méthodologie s’appuyant sur l’analyse d’enregistrements vidéoscopiques, et le développement d’un codage issu du FACS (Facial Action Coding System). Une cohorte de référence a ainsi été constituée. Après avoir validé notre méthodologie pour la caractérisation externe de la mimique, l’analyse des muscles peauciers par l’IRM a été réalisée sur 10 hémifaces parmi les sujets sains issus de la cohorte. Cette caractérisation a fait appel, à partir d’une anatomie in vivo, à une modélisation de certains muscles peauciers (zygomaticus major en particulier) afin d’extraire des paramètres morphologiques, de réaliser une analyse plus fine de la morphologie musculaire en 3 dimensions, et d’apporter une meilleure compréhension du comportement cinématique du muscle dans différentes positions. Par son intégration dans un questionnement plus vaste :- comment caractériser objectivement la mimique faciale ? - quels sont les indicateurs qualitatifs et quantitatifs de la mimique que nous pouvons recueillir, et comment réaliser ce recueil ? - comment utiliser les développements technologiques dans les applications cliniques ? Ce travail constitue une étape préliminaire à d’autres travaux. Il pourra fournir des données de référence à des fins de modélisation, de simulation de la mimique faciale, ou de développements d’outil de mesures pour le suivi et l’évaluation des déficits de la mimique faciale. / The aim of this research is to study facials mimics movements and to correlate externat soft tissue (i.e., cutaneous) movement during facial mimics with internal (i.e., facial mimic muscle) movement. The entire facial mimicry couldn't be studied, that's why relevant movements had been selected. Those movements were characterised by a clinically qualitative analysis in 23 young healthy volunteers. The analysis was performed with video recordings including scaling derived from the FACS (Facial Action Coding System). After the validation of external characterisation by this method, internal characterisation of the mimic facial muscle was carried out in 10 volunteers. A modelization of selected facial mimic muscle as Zygomaticus Major was achieved. With this work, morphological parameters could be extracted, 3D morphometric data were analysed to provide a better understanding of cinematic behaviour of muscle in different positions.This research is included in the Simovi Project, which aims to determine to what extent a facial mimic can be evaluated objectively, to select the qualitative and quantitative indicators for evaluation of mimic facial disorders, and to transfer our technological developments in clinical field. This research is a first step and provides data for simulation or developments of measurement tools in evaluation and follow-up of mimic facial disorders.