Pan X
Department of Radiology, The University of Chicago, IL 60637, USA.
IEEE Trans Med Imaging. 1998 Jun;17(3):395-406. doi: 10.1109/42.712129.
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.
n维（n-D）拉东变换构成了各种断层成像应用的数学基础，它可被视为n-D正弦图空间中的一个n维函数。准确重建连续或离散的断层图像需要在相应的n-D正弦图空间中全面了解拉东变换。然而，在实际中，人们在正弦图空间中只能获得拉东变换的有限离散样本集。人们常常通过调用各种插值算法从其离散样本中推导出所需的拉东变换的全面知识。根据维特克-香农采样定理，从其离散样本中完全且唯一恢复拉东变换的一个必要条件是拉东变换本身是带限的。因此，有必要分析拉东变换的带限特性。在这项工作中，我们明确分析了拉东变换的带限特性，并表明拉东变换在两种定量意义上在数学上是准带限的[或本质上是带限的]，并且在实际中基本上可被视为带限的。准带限特性可用于提高拉东变换的角度采样密度。
