Doctoral Dissertations

Date of Award

5-1998

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Computer Science

Major Professor

Jens Gregor

Committee Members

Michael W. Berry, Michael G. Thomason, Mongi A. Abidi

Abstract

This dissertation develops a computational framework for iterative reconstruction of three-dimensional (3D) Magnetic Resonance Images (MRI) from boron data. The application is Boron Neutron Capture Therapy (BNCT) which is a promising technique for cancer treatment and MRI is used to monitor the various phases of the therapy. Traditionally, boron MRI is carried out by sampling the object’s Fourier spectrum along spherical trajectories and reconstructing the image with interpolation onto a 3D Cartesian grid followed by Fourier inversion. However, this approach does not allow the incorporation of prior spatial knowledge into the reconstruction computation. We therefore propose to reconstruct boron images using iterative algorithms to avoid interpolation in Fourier space as well as to allow for the introduction of spatial constraints.

The spherical data sampling algorithm is modified such that true Radon projection data is obtained and geometrical symmetries are induced. The image is modeled as a linear combination of Kaiser-Bessel basis functions whose 3D Radon transforms are derived. Iterative 3D reconstruction algorithms have vast memory and CPU time requirements. We address this problem by distributing the computation across a network of workstations and by making use of the aforementioned symmetries. Based on the theory of support functions, we propose a 3D focus-of-attention preprocessing technique to further reduce the computational demands. An experimental study based on a noise-free phantom is provided to assess the quality and computational performance of two specific iterative solvers that produce least-squares and maximum-likelihood solutions, respectively. These algorithms are compared with and without focus-of-attention data preprocessing and for different Kaiser-Bessel window parameters. The experiments indicate that the least-squares algorithm converges faster to the true image than the maximum-likelihood algorithm. Finally, it is shown that the combined use of symmetries and focus-of-attention allows us to carry out the 3D image reconstruction using a very small network of workstations.

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