In this thesis, we will study certain generalizations of the classical Shannon Sampling Theorem, which allows for the reconstruction of a pi-band-limited, square-integrable function from its samples on the integers. J. R. Higgins provided a generalization where the integers can be perturbed by less than 1/4, which includes nonuniform and...
Sampling theorems provide exact interpolation formulas for bandlimited
functions. They play a fundamental role in signal processing. A function is called
bandlimited if its Fourier transform vanishes outside a compact set. A generalized
sampling theorem in the framework of locally compact Abelian groups is presented.
Sampling sets are finite unions...
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...
X-ray computed tomography is a noninvasive imaging modality capable of reconstructing exact density values of 3D objects. Computed tomography machines are deployed across the world to provide doctors with an image that reveals more detail than a standard x-ray image. We investigate algorithms based on exact computed tomography reconstruction formulas...
