#### Document Type

Dissertation

#### Date of Degree

Spring 2011

#### Degree Name

PhD (Doctor of Philosophy)

#### Degree In

Applied Mathematical and Computational Sciences

#### First Advisor

Lihe Wang

#### Abstract

X-ray computed tomography is a widely adopted medical imaging method that uses projections to recover the internal image of a subject. Since the invention of X-ray computed tomography in the 1970s, several generations of CT scanners have been developed. As 3D-image reconstruction increases in popularity, the long processing time associated with these machines has to be significantly reduced before they can be practically employed in everyday applications. Parallel computing is a computer science computing technique that utilizes multiple computer resources to process a computational task simultaneously; each resource computes only a part of the whole task thereby greatly reducing computation time. In this thesis, we use parallel computing technology to speed up the reconstruction while preserving the image quality.

Three representative reconstruction algorithms--namely, Katsevich, EM, and Feldkamp algorithms--are investigated in this work. With the Katsevich algorithm, a distributed-memory PC cluster is used to conduct the experiment. This parallel algorithm partitions and distributes the projection data to different computer nodes to perform the computation. Upon completion of each sub-task, the results are collected by the master computer to produce the final image. This parallel algorithm uses the same reconstruction formula as the sequential counterpart, which gives an identical image result.

The parallelism of the iterative CT algorithm uses the same PC cluster as in the first one. However, because it is based on a local CT reconstruction algorithm, which is different from the sequential EM algorithm, the image results are different with the sequential counterpart. Moreover, a special strategy using inhomogeneous resolution was used to further speed up the computation. The results showed that the image quality was largely preserved while the computational time was greatly reduced.

Unlike the two previous approaches, the third type of parallel implementation uses a shared-memory computer. Three major accelerating methods--SIMD (Single instruction, multiple data), multi-threading, and OS (ordered subsets)--were employed to speed up the computation. Initial investigations showed that the image quality was comparable to those of the conventional approach though the computation speed was significantly increased.

#### Keywords

Computed Tomography, Katsevich Algorithm, Local Iterative Algorithm, Parallel Computing, SIMD

#### Pages

105

#### Bibliography

96-105

#### Copyright

Copyright 2011 Junjun Deng