Graduate Thesis Or Dissertation
 

Nonuniform sampling problems in computed tomography

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  • Two problems involving high-resolution reconstruction from nonuniformly sampled data in x-ray computed tomography are addressed. A technique based on the theorem for sampling on unions of shifted lattices is introduced which exploits the symmetry property in two-dimensional fan beam computed tomography and permits the reconstruction of images with twice the resolution as the standard reconstruction by increasing only the number of views per rotation. An estimate is given for the aliasing error committed in the case of non-bandlimited data. Numerical results are presented which demonstrate the improvement in the quality of images from real and simulated data. A mathematical framework is presented for analyzing the longitudinal interpolation problem in three-dimensional multislice helical computed tomography. The problem is viewed as a collection of one-dimensional nonuniform but periodic sampling problems An accurate interpolation formula based on the periodic sampling theorem is introduced. A measure of suitability of a sampling scheme is presented and candidates for so-called preferred helical pitch are identified. Numerical results from simulated data are presented which confirm the theoretical predictions.
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