Series Expansions of the Reconstruction Kernel of the Radon Transform over a Cormack-Type Family of Curves with Applications in Tomography
Series Expansions of the Reconstruction Kernel of the Radon Transform over a Cormack-Type Family of Curves with Applications in Tomography
复制标题
Cormack型曲线族上Radon变换重构核的级数展开及其在层析成像中的应用
DOI：
10.1137/130942784
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Lakhal
中科院分区：
文献类型：
--
作者：
Rigaud;Lakhal
本文研究了一类Cormack型曲线族上的Radon变换，并给出了精确的反演公式。被研究的曲线族被称为，在以前的工作中作为一种合适的流形出现在传统的和康普顿散射层析成像(CST)中的成像概念建模中。更具体地说，用于计算机层析成像(CT)的经典Radon变换的直线、积分支撑点属于。在传统的层析成像中，许多重建技术计算数据的导数，目的是降低与二维Radon变换相关的重建核的奇异性阶数。然而，区分数据需要正则化步骤(例如，用光滑函数卷积)，这降低了重建图像的分辨率。在此，提出的解析反演公式在不对数据进行区分的情况下恢复了被测物体的圆谐分量，从而提高了最终的分辨率。此外，我们还利用Radon变换的值域性质来处理重建核的奇异性问题。由于理论结果是在非常一般的Radon变换反问题的背景下发展的，因此我们的算法在CT和CST领域似乎有很多潜在的应用。在CT框架下和在CST上的一种模式下的数值结果表明，与众所周知的滤波反投影相比，该算法在精度和稳定性方面具有更强的优势。
This paper is concerned with the Radon transform over a family of Cormack-type curves and provides an exact inversion formula. The studied family of curves, called, appeared in previous works as a suitable manifold for modeling imaging concepts in conventional and Compton scattering tomography (CST). More specifically, the straight line, integral support of the classical Radon transform used in computed tomography (CT) belongs to. In conventional tomography, many reconstruction techniques compute the derivative of the data with the aim of reducing the order of singularity of the reconstruction kernel associated here to the Radon transform in two dimensions. However, differentiating data requires a regularization step (for instance, convolution with a smooth function) which reduces the resolution of reconstructed images. Here, the proposed analytical inversion formula recovers the circular harmonic components of the sought object without differentiation of the data, which leads to an improvement of the final resolution. Furthermore, we deal with the singularity issue of the reconstruction kernel by applying a range property of the Radon transform. Since theoretical results are developed in a quite general context of inverse problems for Radon transforms over, the potential applications of our algorithm appear to be numerous in the field of CT and CST. Numerical results in the framework of CT and of one modality on CST reveal the strength of this algorithm in terms of accuracy and stability in comparison with the well-known filtered back-projection.
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关于广义 Cormack 型曲线类的 Radon 变换的反演
影响因子：
2.1
作者：
G. Rigaud
通讯作者：
G. Rigaud
氡气在广义科马克曲线和新的康普顿散射断层扫描模式上进行变换
影响因子：
2.1
作者：
T. Truong;M. Nguyen
通讯作者：
M. Nguyen
将图像重建和图像分析与二维断层扫描应用相结合
DOI：
10.1137/070700863
发表时间：
2008
期刊：
SIAM J. Imaging Sci.
影响因子：
--
作者：
A. Louis
通讯作者：
A. Louis
可逆 Radon 变换的支持曲线
影响因子：
0.6
作者：
Á. Kurusa
通讯作者：
Á. Kurusa
影响因子：
2.1
作者：
A. Cormack
通讯作者：
A. Cormack