满三维图像重建的卷积反投影算法

本文用构造δ序列的方法,给出了一种n维Radon变换反演的卷积反投影算法,证明了该算法在图像的连续点收敛于原图像,当n=2时,就是广泛用于图像重建的卷积反投影算法,由此也给出了卷积反投影方法收敛性的另一种推导。当n=3时,是新的满三维重建的卷积反投影算法,由于三维反演公式具有局部性,该算法对研究三维局部重建有启示。并基于三维情形,利用模拟数据进行了数值仿真,说明该算法是一种有效的三维图像重建算法。

Convolution-backprojection algorithm of fully three-dimensional image reconstruction

In this work, using Dirac delta sequence, we develop an inverse algorithm based on the n-dimensional Radon transform. Our developed algorithm is also of convolution -backprojection type. We also proved that our proposed algorithm is convergent when the image function is continuous on its counterpart point. In 2-dimension, this algorithm is the classical convolution-backprojection algorithm . Therefore, we provide another method with the proof of convergence of FBP-based algorithm. In 3-dimension, this algorithm is a novel algorithm of fully three-dimensional reconstruction. Because the inverse formula of Radon transform in 3-dimension, this algorithm is useful to the research of 3-dimensional local reconstruction. Furthermore, we performed a preliminary numerical experiments to verify our algorithm with three-dimension. The result shows that our proposed algorithm is effective on image reconstruction.