School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel.
IEEE Trans Image Process. 2012 Feb;21(2):733-41. doi: 10.1109/TIP.2011.2164416. Epub 2011 Aug 12.
The discrete Radon transform (DRT) was defined by Abervuch as an analog of the continuous Radon transform for discrete data. Both the DRT and its inverse are computable in O(n(2) log n) operations for images of size n × n. In this paper, we demonstrate the applicability of the inverse DRT for the reconstruction of a 2-D object from its continuous projections. The DRT and its inverse are shown to model accurately the continuum as the number of samples increases. Numerical results for the reconstruction from parallel projections are presented. We also show that the inverse DRT can be used for reconstruction from fan-beam projections with equispaced detectors.
离散 Radon 变换 (DRT) 由 Abervuch 定义为离散数据的连续 Radon 变换的模拟。对于大小为 n×n 的图像，DRT 及其逆变换都可以在 O(n(2)log n) 运算中计算。在本文中，我们展示了逆 DRT 在从连续投影重建 2-D 物体中的应用。随着样本数量的增加，DRT 及其逆变换被证明可以准确地模拟连续统。我们还展示了逆 DRT 可以用于重建具有等距探测器的扇形束投影。
