CT图像重建滤波器的插值核函数构造法及实例

doi:10.12341/jssms22084

系统科学与数学 ›› 2023, Vol. 43 ›› Issue (4): 829-840.DOI: 10.12341/jssms22084

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CT图像重建滤波器的插值核函数构造法及实例

蒋一鸣¹, 邹晶², 胡晓东², 赵金涛³

1. 江苏科技大学自动化学院, 镇江 212100;
2. 天津大学精密仪器与光电子工程学院, 天津 300072;
3. 天津职业技术师范大学自动化与电气工程学院, 天津 300222

收稿日期:2022-01-29 修回日期:2022-10-23 发布日期:2023-03-29
通讯作者: 赵金涛, Email:zjt2019@tju.edu.cn
基金资助:
国家自然科学基金面上项目(61771328), 国家重点研发计划(2017YFB1103900)资助课题.

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蒋一鸣, 邹晶, 胡晓东, 赵金涛. CT图像重建滤波器的插值核函数构造法及实例[J]. 系统科学与数学, 2023, 43(4): 829-840.

JIANG Yiming, ZOU Jing, HU Xiaodong, ZHAO Jintao. CT Image Reconstruction Filter Design Method by Interpolation Kernel Functions and Examples[J]. Journal of Systems Science and Mathematical Sciences, 2023, 43(4): 829-840.

CT Image Reconstruction Filter Design Method by Interpolation Kernel Functions and Examples

JIANG Yiming¹, ZOU Jing², HU Xiaodong², ZHAO Jintao³

1. School of Automation, Jiangsu University of Science and Technology, Zhenjiang 212100;
2. School of Precision Instrument and Opto-Electronics Engineering, Tianjin University, Tianjin 300072;
3. School of Automation and Electrical Engineering, Tianjin University of Technology and Education, Tianjin 300222

Received:2022-01-29 Revised:2022-10-23 Published:2023-03-29

在经典Radon逆变换的基础上, 提出了一种实现Radon逆变换的二阶差商反投影(Second-order Divided-difference Back Projection,SDBP)方法. 对于离散投影数据,利用插值法将离散的投影值采样序列转化为连续的投影函数, 并根据SDBP公式进一步推导出一种基于插值核函数构造的滤波器设计模型.作为该模型的应用, 文章套用三角形函数得到了一类新型滤波器.相比传统的滤波器, 新型滤波器具有调节性能的可控参数,可以根据实际需求增强某些特性, 从而能获得更加理想的重建图像.

关键词： Radon逆变换, CT, 滤波反投影, 插值核函数, Hilbert变换, 滤波器设计, 三角形函数

Based on the classical inverse Radon transform, the Second-order Divideddifference Back Projection (SDBP) method for realizing inverse Radon transform is proposed in this paper. For discrete projection data, the discrete projection sampling sequence is transformed into continuous projection function by data interpolation. Through logical derivation, a filter design model based on interpolation kernel functions is proposed by using SDBP formula. As an application of the filter design model, a new kind of filter is obtained by applying triangle function. Compared with traditional filters, the new filter has controllable parameters to adjust the performance. Such that some features can be enhanced on the basis of actual needs, so as to obtain better reconstructed images.

Key words: Inverse Radon transform, CT, FBP, interpolation kernel function, Hilbert transform, filter design, triangle function

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