A reconstruction algorithm in computerized tomography is a procedure for reconstructing the attenuation coefficientscient, a real-valued function associated with the object of interest, from the measured projection data. Generally speaking, reconstruction algorithms in CT fall into two categories: direct, e.g., filtered back-projection (FBP), or iterative. In this thesis, we discuss a new fast matrix-free iterative reconstruction method based on a polyenergetic model. While most modern x-ray CT scanners rely on the well-known filtered back-projection algorithm, the corresponding reconstructions can be corrupted by beam hardening artifacts. These artifacts arise from the unrealistic physical assumption of monoenergetic x-ray beams. In this thesis, to compensate, we use an alternative model that accounts for differential absorption of polyenergetic x-ray photons and discretize it directly. We do not assume any prior knowledge about the physical properties of the scanned object. We study and implement different solvers and nonlinear unconstrained optimization methods, such as a Newton-like method and an extension of the Levenberg-Marquardt-Fletcher algorithm. We explain how we can use the structure of the Radon matrix and the properties of FBP to make our method matrix-free and fast. Finally, we discuss how we regularize our problem by applying different regularization methods, such as Tikhonov and regularization in the 1-norm. We present numerical reconstructions based on the associated nonlinear discrete formulation incorporating various iterative optimization methods.

A reconstruction algorithm in computerized tomography is a procedure for reconstructing the attenuation coefficientscient, a real-valued function associated with the object of interest, from the measured projection data. Generally speaking, reconstruction algorithms in CT fall into two categories: direct, e.g., filtered back-projection (FBP), or iterative. In this thesis, we discuss a new fast matrix-free iterative reconstruction method based on a polyenergetic model. While most modern x-ray CT scanners rely on the well-known filtered back-projection algorithm, the corresponding reconstructions can be corrupted by beam hardening artifacts. These artifacts arise from the unrealistic physical assumption of monoenergetic x-ray beams. In this thesis, to compensate, we use an alternative model that accounts for differential absorption of polyenergetic x-ray photons and discretize it directly. We do not assume any prior knowledge about the physical properties of the scanned object. We study and implement different solvers and nonlinear unconstrained optimization methods, such as a Newton-like method and an extension of the Levenberg-Marquardt-Fletcher algorithm. We explain how we can use the structure of the Radon matrix and the properties of FBP to make our method matrix-free and fast. Finally, we discuss how we regularize our problem by applying different regularization methods, such as Tikhonov and regularization in the 1-norm. We present numerical reconstructions based on the associated nonlinear discrete formulation incorporating various iterative optimization methods.

Wood is a limited natural resource whose characteristics have been difficult to identify by advanced technology. The most expensive is a hardwood. There is a desire to optimize the production of wood products by minimizing waste and maximizing output. It could be achieved if one had capabilities to evaluate the common wood structures ― knots, rots, empty spaces and other defects. There are many nondestructive testing methods that could be applied to the evaluation of the inner quality of a log. The most successful one is an x-ray computerized tomography. This thesis covers principles of computerized tomography and image reconstruction algorithms. Testing was performed on implementations of tomographic image reconstruction algorithms using synthetic and real data. Research on an application of an x-ray computerized tomography for the analysis of wood structures was made. Inspection of glued zones in glued wooden articles was accomplished using tomographic imaging. Guidelines for the creation of a wood specialized x-ray computerized tomograph were given.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-10-04T19:49:28Z No. of bitstreams: 1 giovannicerronejunior.pdf: 817886 bytes, checksum: 0fa932ad0501da4870ddd992b78ab4e1 (MD5) / Approved for entry into archive by Diamantino Mayra (mayra.diamantino@ufjf.edu.br) on 2016-10-05T10:52:53Z (GMT) No. of bitstreams: 1 giovannicerronejunior.pdf: 817886 bytes, checksum: 0fa932ad0501da4870ddd992b78ab4e1 (MD5) / Made available in DSpace on 2016-10-05T10:52:53Z (GMT). No. of bitstreams: 1 giovannicerronejunior.pdf: 817886 bytes, checksum: 0fa932ad0501da4870ddd992b78ab4e1 (MD5) Previous issue date: 2010-07-30 / Este estudo qualiquantitativo observacional transversal avaliou e comparou a densidade mineral das suturas palatina mediana e zigomaticomaxilar em diferentes faixas etárias por meio de tomografia computadorizada de feixe cônico. Foram analisadas imagens de 72 exames do crânio de indivíduos na faixa etária entre 10 a 40 anos, sem qualquer tipo de malformação ou patologia óssea e que não tivessem passado por tratamento ortodôntico ou ortopédico dos maxilares. As imagens foram divididas em grupos etários: grupo 1 – de 10 a 15 anos; grupo 2 – de 16 a 20 anos; grupo 3 – de 21 a 25 anos; grupo 4 – de 26 a 30 anos; grupo 5 – de 31 a 35 anos e; grupo 6 – de 36 a 40 anos. A sutura palatina mediana foi avaliada em cortes axiais da imagem tomográfica e a sutura zigomaticomaxilar por meio da reconstrução panorâmica. Para calibração do operador foi realizado o erro de método pelo teste de correlação de Pearson e a análise de variância (ANOVA) (p = 0,018). Na obtenção dos resultados foi aplicado o teste de Kolmogorov-Smirnov e a prova de Levenne com nível de significância de 5%. Quanto ao gênero, não foram encontradas diferenças estatisticamente significantes entre indivíduos nos parâmetros avaliados. Os valores de densidade nas regiões de interesse das suturas zigomaticomaxilares direita e esquerda foram estatisticamente maiores do que os valores de densidade nas mesmas regiões da sutura palatina mediana nos grupos 3, 4, 5 e 6 (p < 0,001). Em todos os sítios suturais das imagens tomográficas avaliadas, tanto na sutura palatina mediana quanto nas suturas zigomaticomaxilares direita e esquerda, a densidade mineral sutural foi inferior à densidade da região óssea adjacente, sugerindo que um típico processo de ossificação não ocorreu nestas suturas. A sutura palatina mediana mostrou baixos valores de densidade, em comparação com a sua área óssea adjacente, em todas as idades avaliadas, o que parece ser condizente com suas funções. Os altos índices de densidade encontrados nas suturas zigomaticomaxilares dos indivíduos com idades entre 20 e 40 anos, em comparação com os valores vistos na sutura palatina mediana, sugerem que este pode ser um dos fatores que alteram o comportamento clínico das maxilas frente à expansão maxilar conservadora em adultos. / This cross-sectional observational qualiquantitative study evaluated and compared the mineral density in midpalatal and zigomatic-maxilar sutures in different ages using cone beam computerized tomography. It was analyzed 72 cone beam computerized tomography skull exams from individuals within 10 and 40 years old, without any kind of malformation or bone pathology and that had never been submitted to orthodontic or maxillary orthopedic treatment. Images were separated in age groups: group 1 – from 10 to 15 years; group 2 – from 16 to 20 years; group 3 – from 21 to 25 years; group 4 – from 26 to 30 years; group 5 – from 31 to 35 years; and, group 6 – from 36 to 40 years. Midpalatal suture was analyzed in axial section and zigomatico-maxilar suture by panoramic reconstruction in all individuals. To calibrate de operator it was used Pearson’s correlation test and variance analysis (ANOVA) (p = 0,018). In order to obtain the results it was applied the Kolmogorov-Smirnov test and the Levenne test using 5% significance level. Regarding gender, it was not found statistically significant differences between individuals in the evaluated parameters. Density values in interest regions of right and left zigomatic-maxilar sutures were statistically higher than density values in the same regions of the midpalatal suture in groups 3, 4, 5 and 6 (p < 0,001). In all sutural sites of the images analyzed, both in midpalatal suture and in right and left zigomatic-maxilar sutures, sutural mineral density was inferior to adjacent bone area density, suggesting that a typical ossification process have not occurred. Midpalatal suture showed low density values, comparing to adjacent bone areas, in all ages evaluated, which seems consistent with its functions. High rates of density found in zigomatic-maxilar sutures of the tomographic images of individuals between 20 and 40 years old, comparing to values seen in the midpalatal suture, suggests that it may be one of the factors that change the clinical behavior of the upper jaws during conservative maxillary expansion in adults.