Quasi Band-Limited Properties of Radon Transforms and Their Implications for Increasing Angular Sampling Densities

The n-dimensional (n-D) radon transform, which forms the mathematical basis for a broad variety of tomographic imaging applications, can be viewed as an n-D function in n-D sinogram space. Accurate reconstruction of continuous or discrete tomographic images requires full knowledge of the radon transform in the corresponding n-D sinogram space. In practice, however, one can have only a finite set of discrete samples of the radon transform in the sinogram space. One often derives the desired full knowledge of the radon transform from its discrete samples by invoking various interpolation algorithms. According to the Wittaker-Shannon sampling theorem, a necessary condition for a full and unique recovery of the radon transform from its discrete samples is that the radon transform itself be bandlimited. Therefore, it is necessary to analyze the bandlimited properties of the radon transform. In this work, we analyze explicitly the bandlimited properties of the radon transform and show that the radon transform is mathematically quasi-bandlimited [or essentially bandlimited] in two quantitative senses and can essentially be treated as bandlimited in practice. The quasi-bandlimited properties can be used for increasing the angular sampling density of the radon transform.