Abstract:
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.
