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一种基于二维傅里叶变换的Helgason-Ludwig一致性条件的截断CT数据改进外推方案。

An Improved Extrapolation Scheme for Truncated CT Data Using 2D Fourier-Based Helgason-Ludwig Consistency Conditions.

作者信息

Xia Yan, Berger Martin, Bauer Sebastian, Hu Shiyang, Aichert Andre, Maier Andreas

机构信息

Pattern Recognition Lab, Friedrich-Alexander-University Erlangen-Nuremberg, Erlangen, Germany.

Erlangen Graduate School in Advanced Optical Technologies (SAOT), Erlangen, Germany.

出版信息

Int J Biomed Imaging. 2017;2017:1867025. doi: 10.1155/2017/1867025. Epub 2017 Jul 20.

DOI:10.1155/2017/1867025
PMID:28808441
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC5541827/
Abstract

We improve data extrapolation for truncated computed tomography (CT) projections by using Helgason-Ludwig (HL) consistency conditions that mathematically describe the overlap of information between projections. First, we theoretically derive a 2D Fourier representation of the HL consistency conditions from their original formulation (projection moment theorem), for both parallel-beam and fan-beam imaging geometry. The derivation result indicates that there is a zero energy region forming a double-wedge shape in 2D Fourier domain. This observation is also referred to as the Fourier property of a sinogram in the previous literature. The major benefit of this representation is that the consistency conditions can be efficiently evaluated via 2D fast Fourier transform (FFT). Then, we suggest a method that extrapolates the truncated projections with data from a uniform ellipse of which the parameters are determined by optimizing these consistency conditions. The forward projection of the optimized ellipse can be used to complete the truncation data. The proposed algorithm is evaluated using simulated data and reprojections of clinical data. Results show that the root mean square error (RMSE) is reduced substantially, compared to a state-of-the-art extrapolation method.

摘要

我们通过使用赫尔加松 - 路德维希（HL）一致性条件来改进截断计算机断层扫描（CT）投影的数据外推，该条件从数学上描述了投影之间信息的重叠。首先，我们从其原始公式（投影矩定理）理论上推导出平行束和扇形束成像几何结构下HL一致性条件的二维傅里叶表示。推导结果表明，在二维傅里叶域中存在一个形成双楔形的零能量区域。这一观察结果在先前的文献中也被称为正弦图的傅里叶特性。这种表示的主要优点是可以通过二维快速傅里叶变换（FFT）有效地评估一致性条件。然后，我们提出一种方法，该方法利用来自均匀椭圆的数据外推截断投影，椭圆的参数通过优化这些一致性条件来确定。优化椭圆的前向投影可用于完成截断数据。使用模拟数据和临床数据的重投影对所提出的算法进行评估。结果表明，与一种先进的外推方法相比，均方根误差（RMSE）大幅降低。

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