Iterative CT reconstruction algorithms are superior to the standard convolution backpropagation (CBP) methods when reconstructing from a small number of views (hence less radiation), but are computationally costly. To reduce the execution time, this work implements and tests a parallel approach to iterative algorithms using a cluster of workstations, which is a low cost system found in many offices and non-academic sites. A previous implementation showed little speedup because of the significant cost of inter-processor communication. In this thesis, several data partitioning methods are examined, including some image tiling methods that exploit the spatial locality demonstrated by local CT. Using these methods, computation can proceed locally, without the need for inter-processor communication during every iteration. A relative speedup of up to 17 times is obtained using 25 processors, demonstrating that good performance can be obtained running computationally intensive CT reconstruction algorithms on distributed memory hardware. / October 2007

Iterative CT reconstruction algorithms are superior to the standard convolution backpropagation (CBP) methods when reconstructing from a small number of views (hence less radiation), but are computationally costly. To reduce the execution time, this work implements and tests a parallel approach to iterative algorithms using a cluster of workstations, which is a low cost system found in many offices and non-academic sites. A previous implementation showed little speedup because of the significant cost of inter-processor communication. In this thesis, several data partitioning methods are examined, including some image tiling methods that exploit the spatial locality demonstrated by local CT. Using these methods, computation can proceed locally, without the need for inter-processor communication during every iteration. A relative speedup of up to 17 times is obtained using 25 processors, demonstrating that good performance can be obtained running computationally intensive CT reconstruction algorithms on distributed memory hardware.

The Kaczmarz method is an iterative algorithm that solves overdetermined systems of linear equalities. This paper studies a system of linear equalities and inequalities. We use the block version of the Kaczmarz method applied towards the equalities with the simple randomized Kaczmarz scheme for the inequalities. This primarily involves combining Needell and Tropp's work on the block Kaczmarz method with the application of a randomized Kaczmarz approach towards a system of equalities and inequalities performed by Leventhal and Lewis. We give an expected linear rate of convergence for this kind of system and find that using the block Kaczmarz scheme for the equalities can improve the rate compared to the simple Kaczmarz method.

Iterative CT reconstruction algorithms are superior to the standard convolution backpropagation (CBP) methods when reconstructing from a small number of views (hence less radiation), but are computationally costly. To reduce the execution time, this work implements and tests a parallel approach to iterative algorithms using a cluster of workstations, which is a low cost system found in many offices and non-academic sites. A previous implementation showed little speedup because of the significant cost of inter-processor communication. In this thesis, several data partitioning methods are examined, including some image tiling methods that exploit the spatial locality demonstrated by local CT. Using these methods, computation can proceed locally, without the need for inter-processor communication during every iteration. A relative speedup of up to 17 times is obtained using 25 processors, demonstrating that good performance can be obtained running computationally intensive CT reconstruction algorithms on distributed memory hardware.

This project implements a parallel algorithm for Computed Tomography based on the Algebraic Reconstruction Technique (ART) algorithm. This technique for reconstructing pictures from projections is useful for applications such as Computed Tomography (CT or CAT). The algorithm requires fewer views, and hence less radiation, to produce an image of comparable or better quality. However, the approach is not widely used because of its computationally intensive nature in comparison with rival technologies. A faster ART algorithm could reduce the amount of radiation needed for CT imaging by producing a better image with fewer projections. A reconstruction from projections version of the ART algorithm for two dimensions was implemented in parallel using the Message Passing Interface (MPI) and OpenMP extensions for C. The message passing implementation did not result in faster reconstructions due to prohibitively long and variant communication latency. The shared memory implementation produced positive results, showing a clear computational advantage for multiple processors and measured efficiency ranging from 60-95%. Consistent with the literature, image quality proved to be significantly better compared to the industry standard Filtered Backprojection algorithm especially when reconstructing from fewer projection angles. / October 2006

This project implements a parallel algorithm for Computed Tomography based on the Algebraic Reconstruction Technique (ART) algorithm. This technique for reconstructing pictures from projections is useful for applications such as Computed Tomography (CT or CAT). The algorithm requires fewer views, and hence less radiation, to produce an image of comparable or better quality. However, the approach is not widely used because of its computationally intensive nature in comparison with rival technologies. A faster ART algorithm could reduce the amount of radiation needed for CT imaging by producing a better image with fewer projections. A reconstruction from projections version of the ART algorithm for two dimensions was implemented in parallel using the Message Passing Interface (MPI) and OpenMP extensions for C. The message passing implementation did not result in faster reconstructions due to prohibitively long and variant communication latency. The shared memory implementation produced positive results, showing a clear computational advantage for multiple processors and measured efficiency ranging from 60-95%. Consistent with the literature, image quality proved to be significantly better compared to the industry standard Filtered Backprojection algorithm especially when reconstructing from fewer projection angles.

This project implements a parallel algorithm for Computed Tomography based on the Algebraic Reconstruction Technique (ART) algorithm. This technique for reconstructing pictures from projections is useful for applications such as Computed Tomography (CT or CAT). The algorithm requires fewer views, and hence less radiation, to produce an image of comparable or better quality. However, the approach is not widely used because of its computationally intensive nature in comparison with rival technologies. A faster ART algorithm could reduce the amount of radiation needed for CT imaging by producing a better image with fewer projections. A reconstruction from projections version of the ART algorithm for two dimensions was implemented in parallel using the Message Passing Interface (MPI) and OpenMP extensions for C. The message passing implementation did not result in faster reconstructions due to prohibitively long and variant communication latency. The shared memory implementation produced positive results, showing a clear computational advantage for multiple processors and measured efficiency ranging from 60-95%. Consistent with the literature, image quality proved to be significantly better compared to the industry standard Filtered Backprojection algorithm especially when reconstructing from fewer projection angles.

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Void fraction is an essential parameter for understanding the interfacial structure, and heat and mass transfer mechanisms in various gas-liquid flow systems. It becomes critically important to accurately measure void fraction as advanced high fidelity two-phase flow models require high-quality validation data. However, void fraction measurement remains a challenging task to date due to the complexity and rapid-changing characteristic of the gas-liquid boundary flow structure. This study aims to develop an advanced void fraction measurement system based on x-ray and fast line detector technologies. The dissertation has covered the major components necessary to develop a complete measurement system. Spectral analysis of x-ray attenuation in two-phase flow has been performed, and a new void fraction model is developed based on the analysis. The newly developed pixel-to-radial conversion algorithm is capable of converting measured void fraction along with the detector array to the radial distribution in a circular pipe for a wide range of void fraction conditions. The x-ray system attains the radial distributions of key measurable factors such as void fraction and gas velocity. The data are compared with the double-sensor conductivity probe and gas flowmeter for various flow conditions. The results show reasonable agreements between the x-ray and the other measurement techniques. Finally, various 2-D tomography algorithms are implemented for the non-axisymmetric two-phase flow reconstruction. A comprehensive summary of classical absorption tomography for the two-phase flow study is provided. An in-depth sensitivity study is carried out using synthetic bubbles, aiming to investigate the effect of various uncertainty factors such as background noise, off-center shift, void profile effect, etc. The sensitivity study provides a general guideline for the performance of existing 2-D reconstruction algorithms. / Doctor of Philosophy / Gas-liquid flow phenomenon exists in an extensive range of natural and engineering systems, for example, hydraulic pipelines in a nuclear reactor, heat exchanger, pump cavitation, and boilers in the gas-fired power stations. Accurate measurement of the void fraction is essential to understand the behaviors of the two-phase flow phenomenon. However, measuring void fraction distribution in two-phase flow is a difficult task due to its complex and fast-changing interfacial structure. This study developed a comprehensive suite of the non-intrusive x-ray measurement techniques, and a pixel-to-radial conversion algorithm to process the line- and time-averaged void fraction information. The newly developed algorithm, called the Area-based Onion-Peeling (ABOP) method, can convert the pixel measurement to the radial void fraction distribution, which is more useful for studying and modeling axisymmetric flows. Various flow conditions are measured and evaluated for the benchmarking of the algorithm. Finally, classical 2-D reconstruction algorithms are investigated for the void fraction measurement in non-axisymmetric flows. A comprehensive summary of the performance of these algorithms for a two-phase flow study is provided. An in-depth sensitivity study using synthetic bubbles has been performed to examine the effect of uncertainty factors and to benchmark the algorithms for the non-axisymmetric flows.