In X-ray computed tomography, motion of the object (breathing, for example) while X-ray projections are acquired for tomographic reconstruction leads to mo- tion artifacts in the reconstructed image. Object motion (such as that of breathing lungs) during acquisition of a computed tomography scan causes artifacts in the reconstructed image due to the reason that the source and detectors require a finite amount of time to rotate around the object while acquiring measurements even as the object is changing with time. With traditional reconstruction algorithms, the object is assumed to be stationary while data is acquired. However, in the case of dynamic tomography, the projection data that is acquired is not consistent, as it is data measured from an object that is deformed at each view angle of measurement. In this work, we propose a method for estimation of general (non-rigid) small motion for dynamic tomography from motion-corrupted projection data. For a static object, the Helgason-Ludwig consistency conditions impose some structure on the moments of the projections. However in the case of dynamic object (result- ing in motion-corrupted projections) this is violated. In the proposed method, we estimate motion parameters of the general motion model from the moments of the dynamic projections. The dynamic object can be modeled as f (g(x, t)) where g is a time-dependent warping function. The non-linear problem of solving a system involving composition of functions is dealt with in the Fourier transform space where it simplifies into a problem involving multiplicatively separable functions. The system is then linearized to solve for object motion. We assume a general basis function in our model. For numerical simulations, we use polynomial and B-spline basis functions as special cases of the basis functions. Simulation is performed by applying known deformations to the Shepp-Logan phantom, to a head slice of the Visible Human phantom and a thorax slice of the Zubal phantom. Simulations are performed for projections generated by parallel- beam and fan-beam geometry. Simulation for fan-beam geometry are performed by rebinning the motion corrupted fan beam projections to parallel beam projections, followed by the proposed motion estimation method. Simulation for the Visible Human phantom and the thorax slice of the Zubal phantom are performed for fan- beam geometry. Poisson noise is also added to the generated dynamic projections before motion estimation is performed. To solve the ill-posed problem of motion estimation by the proposed method, we use a Tikhonov type regularization that involves minimizing an objective function that is the sum of a data discrepancy term, a term that penalizes temporal variation of motion, and another term to penalize large magnitudes of motion. Using the estimated motion, the original image has been reconstructed from the motion corrupted projection data, with the knowledge of the underlying motion which is estimated by the proposed algorithm, by an algebraic technique similar to the dynamic SART algorithm from the literature. Here, a SART-type coefficient matrix is computed using ray tracing with rays whose paths are warped according to the estimated motion. The dynamic image at t = 0 is then reconstructed with using the computed dynamic SART matrix.

Submitted by Rafael Santana (rafael.silvasantana@ufpe.br) on 2017-05-11T18:10:34Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Versão Atualizada Tese Eric Ferreira de Oliveira.pdf: 1865683 bytes, checksum: 517608a245f6372afd45b3bba78733d6 (MD5) / Made available in DSpace on 2017-05-11T18:10:34Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Versão Atualizada Tese Eric Ferreira de Oliveira.pdf: 1865683 bytes, checksum: 517608a245f6372afd45b3bba78733d6 (MD5) Previous issue date: 2016-02-29 / CNEN / O estado da arte dos métodos aplicados para processos industriais é atualmente baseado em princípios de reconstruções tomográficas clássicas desenvolvidos para padrões tomográficos de distribuições estáticas, ou seja, são limitados a processos de pouca variabilidade. Ruídos e artefatos de movimento são os principais problemas causados pela incompatibilidade nos dados gerada pelo movimento. Além disso, em processos tomográficos industriais é comum um número limitado de dados podendo produzir ruído, artefatos e não concordância com a distribuição em estudo. Um dos objetivos do presente trabalho é discutir as dificuldades que surgem da implementação de algoritmos de reconstrução em tomografia dinâmica que foram originalmente desenvolvidos para distribuições estáticas. Outro objetivo é propor soluções que visam reduzir a perda de informação temporal devido a utilização de técnicas estáticas em processos dinâmicos. No que diz respeito à reconstrução de imagem dinâmica foi realizada uma comparação entre diferentes métodos de reconstrução estáticos, como MART e FBP, quando usado para cenários dinâmicos. Esta comparação foi baseada em simulações por MCNPX, e também analiticamente, de um cilindro de alumínio que se move durante o processo de aquisição, e também com base em imagens de cortes transversais de técnicas de CFD. Outra contribuição foi aproveitar o canal triplo de cores necessário para exibir imagens coloridas na maioria dos monitores, de modo que, dimensionando adequadamente os valores adquiridos de cada vista no sistema linear de reconstrução, foi possível imprimir traços temporais na imagem tradicionalmente reconstruída. Finalmente, uma técnica de correção de movimento usado no campo da medicina foi proposto para aplicações industriais, considerando-se que a distribuição de densidade nestes cenários pode apresentar variações compatíveis com movimentos rígidos ou alterações na escala de certos objetos. A ideia é usar dados conhecidos a priori ou durante o processo, como vetor deslocamento, e então usar essas informações para melhorar a qualidade da reconstrução. Isto é feito através da manipulação adequada da matriz peso no método algébrico, isto é, ajustando-se os valores para refletir o movimento objeto do previsto ou deformação. Os resultados de todas essas técnicas aplicadas em vários experimentos e simulações são discutidos neste trabalho. / The state of the art methods applied to industrial processes is currently based on the principles of classical tomographic reconstructions developed for tomographic patterns of static distributions, or is limited to cases of low variability of the density distribution function of the tomographed object. Noise and motion artifacts are the main problems caused by a mismatch in the data from views acquired in different instants. All of these add to the known fact that using a limited amount of data can result in the presence of noise, artifacts and some inconsistencies with the distribution under study. One of the objectives of the present work is to discuss the difficulties that arise from implementing reconstruction algorithms in dynamic tomography that were originally developed for static distributions. Another objective is to propose solutions that aim at reducing a temporal type of information loss caused by employing regular acquisition systems to dynamic processes. With respect to dynamic image reconstruction it was conducted a comparison between different static reconstruction methods, like MART and FBP, when used for dynamic scenarios. This comparison was based on a MCNPx simulation as well as an analytical setup of an aluminum cylinder that moves along the section of a riser during the process of acquisition, and also based on cross section images from CFD techniques. As for the adaptation of current tomographic acquisition systems for dynamic processes, this work established a sequence of tomographic views in a just-in-time fashion for visualization purposes, a form of visually disposing density information as soon as it becomes amenable to image reconstruction. A third contribution was to take advantage of the triple color channel necessary to display colored images in most displays, so that, by appropriately scaling the acquired values of each view in the linear system of the reconstruction, it was possible to imprint a temporal trace into the regularly reconstructed image, where the temporal trace utilizes a channel and the regular reconstruction utilizes a different one. Finally, a motion correction technique used in the medical field was proposed for industrial applications, considering that the density distribution in these scenarios may present variations compatible with rigid motions or changes in scale of certain objects. The idea is to identify in some configurations of the temporarily distributed data clues of the type of motion or deformation suffered by the object during the data acquisition, and then use this information to improve the quality of the reconstruction. This is done by appropriately manipulating the weight matrix in the algebraic method, i.e., by adjusting the values to reflect the predicted object motion or deformation. The results of all these techniques applied in several experiments and simulations are discussed in this work.

La tomographie est la discipline qui cherche à reconstruire une donnée physique dans son volume, à partir de l’information indirecte de projections intégrées de l’objet, à différents angles de vue. L’une de ses applications les plus répandues, et qui constitue le cadre de cette thèse, est l’imagerie scanner par rayons X pour le médical. Or, les mouvements inhérents à tout être vivant, typiquement le mouvement respiratoire et les battements cardiaques, posent de sérieux problèmes dans une reconstruction classique. Il est donc impératif d’en tenir compte, i.e. de reconstruire le sujet imagé comme une séquence spatio-temporelle traduisant son “évolution anatomique” au cours du temps : c’est la tomographie dynamique. Élaborer une méthode de reconstruction spécifique à ce problème est un enjeu majeur en radiothérapie, où la localisation précise de la tumeur dans le temps est un prérequis afin d’irradier les cellules cancéreuses en protégeant au mieux les tissus sains environnants. Des méthodes usuelles de reconstruction augmentent le nombre de projections acquises, permettant des reconstructions indépendantes de plusieurs phases de la séquence échantillonnée en temps. D’autres compensent directement le mouvement dans la reconstruction, en modélisant ce dernier comme un champ de déformation, estimé à partir d’un jeu de données d’acquisition antérieur. Nous proposons dans ce travail de thèse une approche nouvelle ; se basant sur la théorie des problèmes inverses, nous affranchissons la reconstruction dynamique du besoin d’accroissement de la quantité de données, ainsi que de la recherche explicite du mouvement, elle aussi consommatrice d’un surplus d’information. Nous reconstruisons la séquence dynamique à partir du seul jeu de projections courant, avec pour seules hypothèses a priori la continuité et la périodicité du mouvement. Le problème inverse est alors traité rigoureusement comme la minimisation d’un terme d’attache aux données et d’une régularisation. Nos contributions portent sur la mise au point d’une méthode de reconstruction adaptée à l’extraction optimale de l’information compte tenu de la parcimonie des données — un aspect typique du problème dynamique — en utilisant notamment la variation totale (TV) comme régularisation. Nous élaborons un nouveau modèle de projection tomographique précis et compétitif en temps de calcul, basé sur des fonctions B-splines séparables, permettant de repousser encore la limite de reconstruction imposée par la parcimonie. Ces développements sont ensuite insérés dans un schéma de reconstruction dynamique cohérent, appliquant notamment une régularisation TV spatio-temporelle efficace. Notre méthode exploite ainsi de façon optimale la seule information courante à disposition ; de plus sa mise en oeuvre fait preuve d’une grande simplicité. Nous faisons premièrement la démonstration de la force de notre approche sur des reconstructions 2-D+t à partir de données simulées numériquement. La faisabilité pratique de notre méthode est ensuite établie sur des reconstructions 2-D et 3-D+t à partir de données physiques “réelles”, acquises sur un fantôme mécanique et sur un patient / Computerized tomography (CT) aims at the retrieval of 3-D information from a set of projections acquired at different angles around the object of interest (OOI). One of its most common applications, which is the framework of this Ph.D. thesis, is X-ray CT medical imaging. This reconstruction can be severely impaired by the patient’s breath (respiratory) motion and cardiac beating. This is a major challenge in radiotherapy, where the precise localization of the tumor is a prerequisite for cancer cells irradiation with preservation of surrounding healthy tissues. The field of methods dealing with the reconstruction of a dynamic sequence of the OOI is called Dynamic CT. Some state-of-the-art methods increase the number of projections, allowing an independent reconstruction of several phases of the time sampled sequence. Other methods use motion compensation in the reconstruction, by a beforehand estimation on a previous data set, getting the explicit motion through a deformation model. Our work takes a different path ; it uses dynamic reconstruction, based on inverse problems theory, without any additional information, nor explicit knowledge of the motion. The dynamic sequence is reconstructed out of a single data set, only assuming the motion’s continuity and periodicity. This inverse problem is considered as a minimization of an error term combined with a regularization. One of the most original features of this Ph.D. thesis, typical of dynamic CT, is the elaboration of a reconstruction method from very sparse data, using Total Variation (TV) as a very efficient regularization term. We also implement a new rigorously defined and computationally efficient tomographic projector, based on B-splines separable functions, outperforming usual reconstruction quality in a data sparsity context. This reconstruction method is then inserted into a coherent dynamic reconstruction scheme, applying an efficient spatio-temporal TV regularization. Our method exploits current data information only, in an optimal way ; moreover, its implementation is rather straightforward. We first demonstrate the strength of our approach on 2-D+t reconstructions from numerically simulated dynamic data. Then the practical feasibility of our method is established on 2-D and 3-D+t reconstructions of a mechanical phantom and real patient data