L'imagerie par résonance magnétique (IRM) est un outil remarquable pour le diagnostic clinique, aussi bien pour l'imagerie cérébrale que pour l'imagerie cardiaque et abdominale. C'est notamment la seule modalité d'imagerie qui permet de visualiser et de caractériser l'oedème myocardique. Cependant, la gestion du mouvement reste un problème récurrent en IRM cardiaque. Tant le battement cardiaque que la respiration nécessitent une prise en compte attentive lors de l'acquisition des images et limitent la résolution temporelle et spatiale accessible en pratique clinique courante. L'approche adoptée dans ce travail propose d'intégrer ces mouvements physiologiques dans le processus de reconstruction des images et permet ainsi de réaliser des explorations cardiaques en respiration libre. Un algorithme de reconstruction itératif, corrigeant les mouvements estimés par un modèle contraint par les signaux physiologiques, est dans un premier temps appliqué à l'imagerie cardiaque morphologique. Ses performances vis-à-vis d'une méthode semi-automatique de détection de l'oedème sont évaluées. Il a également été utilisé en association avec une méthode d'acquisition adaptative, afin de permettre l'acquisition d'images en télésystole et en respiration libre. Dans un deuxième temps, cette méthode a été étendue à la quantification du temps de relaxation transversale T2. La cartographie T2 du coeur fournit en effet une caractérisation de l'oedème myocardique. La méthode de reconstruction présentée, ARTEMIS, permet de réaliser cette cartographie en respiration libre et sans allongement du temps d'examen. Ces méthodes exploitent des signaux physiologiques afin d'estimer le mouvement ayant eu lieu pendant l'acquisition. Différentes solutions pour obtenir ces informations physiologiques ont donc également été explorées. Parmi elles, les capteurs à base d'accéléromètres permettent de multiplier les points de mesure alors que les informations "embarquées" dans la séquence d'acquisition IRM ("navigateur") facilitent le déploiement de ces techniques puisqu'elles évitent de recourir à des équipements supplémentaires. Ainsi pendant ces travaux, des méthodes de reconstruction adaptatives ont été développées afin de corriger le mouvement et de prendre en compte les spécificités de chaque patient. Ces travaux ouvrent la voie de l'imagerie par résonance magnétique cardiaque en respiration libre dans un contexte clinique / Magnetic resonance imaging (MRI) is a valuable tool for the clinical diagnosis for brain imaging as well as cardiac and abdominal imaging. For instance, MRI is the only modality that enables the visualization and characterization myocardial edema. However, motion remains a challenging problem for cardiac MRI. Breathing as well as cardiac beating have to be carefully handled during patient examination. Moreover they limit the achievable temporal and spatial resolution of the images. In this work an approach that takes these physiological motions into account during image reconstruction process has been proposed. It allows performing cardiac examination while breathing freely. First, an iterative reconstruction algorithm, that compensates motion estimated from a motion model constrained by physiological signals, is applied to morphological cardiac imaging. A semi-automatic method for edema detection has been tested on reconstructed images. It has also been associated with an adaptive acquisition strategy which enables free-breathing end-systolic imaging. This reconstruction has then been extended to the assessment of transverse relaxation times T2, which is used for myocardial edema characterization. The proposed method, ARTEMIS, enables free-breathing T2 mapping without additional acquisition time. The proposed free breathing approaches take advantage of physiological signals to estimate the motion that occurs during MR acquisitions. Several solutions have been tested to measure this information. Among them, accelerometer-based external sensors allow local measurements at several locations. Another approach consists in the use of k-space based measurements, which are "embedded" inside the MRI pulse sequence (navigator) and prevent from the requirement of additional recording hardware. Hence, several adaptive reconstruction algorithms were developed to obtain diagnostic information from free breathing acquisitions. These works allow performing efficient and accurate free breathing cardiac MRI

Existe na indústria o interesse em utilizar as informações da tomografia computadorizada a fim de conhecer o interior (i) dos objetos industriais fabricados ou (ii) das máquinas e seus meios de produção. Nestes casos, a tomografia tem como finalidade (a) controlar a qualidade do produto final e (b) otimizar a produção, contribuindo na fase piloto dos projetos e na análise da qualidade dos meios sem interromper a produção. O contínuo controle de qualidade dos meios de produção é a chave mestra para garantir a qualidade e a competitividade dos produtos. O Centro de Tecnologia das Radiações (CTR), do Instituto de Pesquisas Energéticas e Nucleares (IPEN/CNEN-SP) vem desenvolvendo esta tecnologia para fins de análises de processos industriais há algum tempo. Atualmente, o laboratório tem desenvolvido três gerações de tomógrafos: (i) primeira geração; (ii) terceira geração; e (iii) tomógrafo Instant Non-Scanning. Os algoritmos de reconstrução de imagens tomográficas tem uma importância relevante para o funcionamento ideal desta tecnologia. Nesta tese, foram desenvolvidos e analisados os algoritmos de reconstrução de imagens tomográficas para serem implementados aos protocolos experimentais dos tomógrafos. Os métodos de reconstrução de imagem analítico e iterativo foram desenvolvidos utilizando o software Matlab® r2013b. Os algoritmos iterativos apresentaram imagens com melhor resolução espacial comparado com as obtidas pelo método analítico. Entretanto as imagens por método analítico apresentaram menos ruídos. O tempo para obtenção de imagem pelo método iterativo é relativamente elevado, e aumenta conforme aumenta a matriz de pixels da imagem. Já o método analítico fornece imagens instantâneas. Para as reconstruções de imagens utilizando o tomógrafo Instant Non-Scanning, as imagens pelo método analítico não apresentaram qualidade de imagem satisfatória comparada aos métodos iterativos. / There is an interest in the industry to use the CT information in order to know the interior (i) of the manufactured industrial objects or (ii) the machines and their means of production. In these cases, the purpose of the tomography systems is to (a) control the quality of the final product and (b) to optimize production, contributing to the pilot phase of the projects and to analyze the quality of the means without interrupting he line production. Continuous quality assurance of the means of production is the key to ensuring product quality and competitiveness. The Radiation Technology Center of the Nuclear and Energy Research Institute (IPEN/CNEN-SP) has been developing this technology for the purpose of industrial analysis. Currently the laboratory has developed three generations of tomography systems: (i) first generation; (ii) third generation; and (iii) Instant Non-Scanning tomography. The algorithms for the reconstruction of tomographic images are of relevant importance for the optimal functioning of this technology. In this PhD thesis, the reconstruction algorithms of tomographic images were developed and analyzed to be implemented to the tomography systems developed. The analytical and iterative image reconstruction methods were developed using the software Matlab® r2013b. The iterative algorithms presented images with better spatial resolution compared to those obtained by the analytical method; however the images of the analytical method presented be less image noisy. The time to obtain the image by the iterative method is high, and increases as the image matrix increases, while the analytical method provides fast images. For images reconstructions using the Instant Non-Scanning tomography system, the images by the analytical method did not present satisfactory image quality compared to the iterative methods.

Existe na indústria o interesse em utilizar as informações da tomografia computadorizada a fim de conhecer o interior (i) dos objetos industriais fabricados ou (ii) das máquinas e seus meios de produção. Nestes casos, a tomografia tem como finalidade (a) controlar a qualidade do produto final e (b) otimizar a produção, contribuindo na fase piloto dos projetos e na análise da qualidade dos meios sem interromper a produção. O contínuo controle de qualidade dos meios de produção é a chave mestra para garantir a qualidade e a competitividade dos produtos. O Centro de Tecnologia das Radiações (CTR), do Instituto de Pesquisas Energéticas e Nucleares (IPEN/CNEN-SP) vem desenvolvendo esta tecnologia para fins de análises de processos industriais há algum tempo. Atualmente, o laboratório tem desenvolvido três gerações de tomógrafos: (i) primeira geração; (ii) terceira geração; e (iii) tomógrafo Instant Non-Scanning. Os algoritmos de reconstrução de imagens tomográficas tem uma importância relevante para o funcionamento ideal desta tecnologia. Nesta tese, foram desenvolvidos e analisados os algoritmos de reconstrução de imagens tomográficas para serem implementados aos protocolos experimentais dos tomógrafos. Os métodos de reconstrução de imagem analítico e iterativo foram desenvolvidos utilizando o software Matlab® r2013b. Os algoritmos iterativos apresentaram imagens com melhor resolução espacial comparado com as obtidas pelo método analítico. Entretanto as imagens por método analítico apresentaram menos ruídos. O tempo para obtenção de imagem pelo método iterativo é relativamente elevado, e aumenta conforme aumenta a matriz de pixels da imagem. Já o método analítico fornece imagens instantâneas. Para as reconstruções de imagens utilizando o tomógrafo Instant Non-Scanning, as imagens pelo método analítico não apresentaram qualidade de imagem satisfatória comparada aos métodos iterativos. / There is an interest in the industry to use the CT information in order to know the interior (i) of the manufactured industrial objects or (ii) the machines and their means of production. In these cases, the purpose of the tomography systems is to (a) control the quality of the final product and (b) to optimize production, contributing to the pilot phase of the projects and to analyze the quality of the means without interrupting he line production. Continuous quality assurance of the means of production is the key to ensuring product quality and competitiveness. The Radiation Technology Center of the Nuclear and Energy Research Institute (IPEN/CNEN-SP) has been developing this technology for the purpose of industrial analysis. Currently the laboratory has developed three generations of tomography systems: (i) first generation; (ii) third generation; and (iii) Instant Non-Scanning tomography. The algorithms for the reconstruction of tomographic images are of relevant importance for the optimal functioning of this technology. In this PhD thesis, the reconstruction algorithms of tomographic images were developed and analyzed to be implemented to the tomography systems developed. The analytical and iterative image reconstruction methods were developed using the software Matlab® r2013b. The iterative algorithms presented images with better spatial resolution compared to those obtained by the analytical method; however the images of the analytical method presented be less image noisy. The time to obtain the image by the iterative method is high, and increases as the image matrix increases, while the analytical method provides fast images. For images reconstructions using the Instant Non-Scanning tomography system, the images by the analytical method did not present satisfactory image quality compared to the iterative methods.

Dual-energy computed tomography (DECT) has shown great potential in the reduction of uncertainties of proton ranges and low energy photon cross section estimation used in radiation therapy planning. The work presented herein investigated three contributions for advancing DECT applications. 1) A linear and separable two-parameter DECT, the basis vector model (BVM) was used to estimate proton stopping power. Compared to other nonlinear two-parameter models in the literature, the BVM model shows a comparable accuracy achieved for typical human tissues. This model outperforms other nonlinear models in estimations of linear attenuation coefficients. This is the first study to clearly illustrate the advantages of linear model not only in accurately mapping radiological quantities for radiation therapy, but also in providing a unique model for accurate linear forward projection modelling, which is needed by the statistical iterative reconstruction (SIR) and other advanced DECT reconstruction algorithms. 2) Accurate DECT requires knowledge of x-ray beam properties. Using the Birch-Marshall1 model and beam hardening correction coefficients encoded in a CT scanner’s sinogram header files, an efficient and accurate way to estimate the x-ray spectrum is proposed. The merits of the proposed technique lie in requiring no physical transmission measurement after a one-time calibration against an independently measured spectrum. This technique can also be used in monitoring the aging of x-ray CT tubes. 3) An iterative filtered back projection with anatomical constraint (iFBP-AC) algorithm was also implemented on a digital phantom to evaluate its ability in mitigating beam hardening effects and supporting accurate material decomposition for in vivo imaging of photon cross section and proton stopping power. Compared to iFBP without constraints, both algorithms demonstrate high efficiency of convergence. For an idealized digital phantom, similar accuracy was observed under a noiseless situation. With clinically achievable noise level added to the sinograms, iFBP-AC greatly outperforms iFBP in prediction of photon linear attenuation at low energy, i.e., 28 keV. The estimated mean errors of iFBP and iFBP-AC for cortical bone are 1% and 0.7%, respectively; the standard deviations are 0.6% and 5%, respectively. The achieved accuracy of iFBP-AC shows robustness versus contrast level. Similar mean errors are maintained for muscle tissue. The standard deviation achieved by iFBP-AC is 1.2%. In contrast, the standard deviation yielded by iFBP is about 20.2%. The algorithm of iFBP-AC shows potential application of quantitative measurement of DECT. The contributions in this thesis aim to improve the clinical performance of DECT.

Ill-posed sets of linear equations typically arise when discretizing certain types of integral transforms. A well known example is image reconstruction, which can be modeled using the Radon transform. After expanding the solution into a finite series of basis functions a large, sparse and ill-conditioned linear system occurs. We consider the solution of such systems. In particular we study a new class of iteration methods named DROP (for Diagonal Relaxed Orthogonal Projections) constructed for solving both linear equations and linear inequalities. This class can also be viewed, when applied to linear equations, as a generalized Landweber iteration. The method is compared with other iteration methods using test data from a medical application and from electron microscopy. Our theoretical analysis include convergence proofs of the fully-simultaneous DROP algorithm for linear equations without consistency assumptions, and of block-iterative algorithms both for linear equations and linear inequalities, for the consistent case. When applying an iterative solver to an ill-posed set of linear equations the error usually initially decreases but after some iterations, depending on the amount of noise in the data, and the degree of ill-posedness, it starts to increase. This phenomenon is called semi-convergence. We study the semi-convergence performance of Landweber-type iteration, and propose new ways to specify the relaxation parameters. These are computed so as to control the propagated error. We also describe a class of stopping rules for Landweber-type iteration for solving linear inverse problems. The class includes the well known discrepancy principle, and the monotone error rule. We unify the error analysis of these two methods. The stopping rules depend critically on a certain parameter whose value needs to be specified. A training procedure is therefore introduced for securing robustness. The advantages of using trained rules are demonstrated on examples taken from image reconstruction from projections. Kaczmarz's method, also called ART (Algebraic Reconstruction Technique) is often used for solving the linear system which appears in image reconstruction. This is a fully sequential method. We examine and compare ART and its symmetric version. It is shown that the cycles of symmetric ART, unlike ART, converge to a weighted least squares solution if and only if the relaxation parameter lies between zero and two. Further we show that ART has faster asymptotic rate of convergence than symmetric ART. Also a stopping criterion is proposed and evaluated for symmetric ART. We further investigate a class of block-iterative methods used in image reconstruction. The cycles of the iterative sequences are characterized in terms of the original linear system. We define symmetric block-iteration and compare the behavior of symmetric and non-symmetric block-iteration. The results are illustrated using some well-known methods. A stopping criterion is offered and assessed for symmetric block-iteration.

Topology-related issues are becoming increasingly important in Computer Graphics. This research examines the use of topological analysis for solving two important problems in 3D Graphics: surface parameterization, and vector field design on surfaces. Many applications, such as high-quality and interactive image synthesis, benefit from the solutions to these problems. Surface parameterization refers to segmenting a 3D surface into a number of patches and unfolding them onto a plane. A surface parameterization allows surface properties to be sampled and stored in a texture map for high-quality and interactive display. One of the most important quality measurements for surface parameterization is stretch, which causes an uneven sampling rate across the surface and needs to be avoided whenever possible. In this thesis, I present an automatic parameterization technique that segments the surface according to the handles and large protrusions in the surface. This results in a small number of large patches that can be unfolded with relatively little stretch. To locate the handles and large protrusions, I make use of topological analysis of a distance-based function on the surface. Vector field design refers to creating continuous vector fields on 3D surfaces with control over vector field topology, such as the number and location of the singularities. Many graphics applications make use of an input vector field. The singularities in the input vector field often cause visual artifacts for these applications, such as texture synthesis and non-photorealistic rendering. In this thesis, I describe a vector field design system for both planar domains and 3D mesh surfaces. The system provides topological editing operations that allow the user to control the number and location of the singularities in the vector field. For the system to work for 3D meshes surface, I present a novel piecewise interpolating scheme that produces a continuous vector field based on the vector values defined at the vertices of the mesh. I demonstrate the effectiveness of the system through several graphics applications: painterly rendering of still images, pencil-sketches of surfaces, and texture synthesis.

Recently, the use of permanent magnets as magnetic field sources in biomedical applications has become widespread. However, usage of permanent magnets in magnetic resonance imaging (MRI) is limited due to their inhomogeneous magnetic field distributions. In this thesis, shape and geometry optimization of a magnet is performed. Moreover, placement of more than one magnet is optimized to obtain desired magnetic field distribution in specific region of space. However, obtained magnetic field distribution can not be used in the conventional MRI image reconstruction techniques. Consequently, an image reconstruction technique for MRI in inhomogeneous magnetic fields is developed. Apart from these, since any reconstruction technique requires signal data, an MRI simulator in inhomogeneous magnetic fields is constructed as a part of this thesis. Obtained results show that the theory developed in this thesis is valid. Consequently, new MRI devices that have permanent magnets as magnetic field sources can be constructed in the future.

No description available.

No description available.

En radiothérapie, la tomodensitométrie (CT) fournit l’information anatomique du patient utile au calcul de dose durant la planification de traitement. Afin de considérer la composition hétérogène des tissus, des techniques de calcul telles que la méthode Monte Carlo sont nécessaires pour calculer la dose de manière exacte. L’importation des images CT dans un tel calcul exige que chaque voxel exprimé en unité Hounsfield (HU) soit converti en une valeur physique telle que la densité électronique (ED). Cette conversion est habituellement effectuée à l’aide d’une courbe d’étalonnage HU-ED. Une anomalie ou artefact qui apparaît dans une image CT avant l’étalonnage est susceptible d’assigner un mauvais tissu à un voxel. Ces erreurs peuvent causer une perte cruciale de fiabilité du calcul de dose. Ce travail vise à attribuer une valeur exacte aux voxels d’images CT afin d’assurer la fiabilité des calculs de dose durant la planification de traitement en radiothérapie. Pour y parvenir, une étude est réalisée sur les artefacts qui sont reproduits par simulation Monte Carlo. Pour réduire le temps de calcul, les simulations sont parallélisées et transposées sur un superordinateur. Une étude de sensibilité des nombres HU en présence d’artefacts est ensuite réalisée par une analyse statistique des histogrammes. À l’origine de nombreux artefacts, le durcissement de faisceau est étudié davantage. Une revue sur l’état de l’art en matière de correction du durcissement de faisceau est présentée suivi d’une démonstration explicite d’une correction empirique. / Computed tomography (CT) is widely used in radiotherapy to acquire patient-specific data for an accurate dose calculation in radiotherapy treatment planning. To consider the composition of heterogeneous tissues, calculation techniques such as Monte Carlo method are needed to compute an exact dose distribution. To use CT images with dose calculation algorithms, all voxel values, expressed in Hounsfield unit (HU), must be converted into relevant physical parameters such as the electron density (ED). This conversion is typically accomplished by means of a HU-ED calibration curve. Any discrepancy (or artifact) that appears in the reconstructed CT image prior to calibration is susceptible to yield wrongly-assigned tissues. Such tissue misassignment may crucially decrease the reliability of dose calculation. The aim of this work is to assign exact physical values to CT image voxels to insure the reliability of dose calculation in radiotherapy treatment planning. To achieve this, origins of CT artifacts are first studied using Monte Carlo simulations. Such simulations require a lot of computational time and were parallelized to run efficiently on a supercomputer. An sensitivity study on HU uncertainties due to CT artifacts is then performed using statistical analysis of the image histograms. Beam hardening effect appears to be the origin of several artifacts and is specifically addressed. Finally, a review on the state of the art in beam hardening correction is presented and an empirical correction is exposed in detail.