基于FDK补偿项与双光源加权的锥束CT伪影抑制方法

向荣林; 张丽

doi:10.15953/j.ctta.2024.222

基于FDK补偿项与双光源加权的锥束CT伪影抑制方法

向荣林^{1, 2,},
张丽^{1, 2, 3, ,}

1.
清华大学工程物理系，北京 100084
2.
粒子技术与辐射成像教育部重点实验室，北京 100084
3.
危爆物品扫描探测国家工程实验室，北京 100084

基金项目: 融合动态能谱与个性化建模的冠状动脉容积成像方法与关键技术重点项目（62031020）。

详细信息

作者简介:
向荣林，男，清华大学工程物理系粒子信息获取与处理研究室在读博士生，主要从事CT重建相关算法研究，E-mail：xiangrl24@163.com

通讯作者:
张丽✉，女，清华大学工程物理系粒子信息获取与处理研究室主任、首席研究员，E-mail：zli@mail.tsinghua.edu.cn。

中图分类号: TP 391.41；R 814.3
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出版历程
- 收稿日期: 2024-10-14
- 修回日期: 2024-11-30
- 录用日期: 2025-01-07
- 网络出版日期: 2025-02-17

Suppression Method for Cone-Beam CT Artifact Based on FDK Compensation and Dual-Source Weighting

XIANG Ronglin^{1, 2,},
ZHANG Li^{1, 2, 3, ,}

1.
Department of Engineering Physics, Tsinghua University, Beijing 100084, China
2.
Key Laboratory of Particle & Radiation Imaging (Tsinghua University), Ministry of Education, Beijing 100084, China
3.
National Engineering Laboratory for Dangerous Articles and Explosives Detection Technologies, Beijing 100084, China

摘要

摘要:
FDK算法具有结构简单、计算速度快、重建质量高等优点，至今仍是锥束CT解析重建的主流算法。然而，若重建点锥角过大，会出现密度下降的锥束伪影。为此学界提出了许多抑制伪影的方法，包括投影加权、束线重排与引入补偿项等，其中引入补偿项的方法计算效率高，并在锥角为十余度的情形取得了良好的伪影抑制效果，在诸多算法中具有一定的优势。然而，对于更大的锥角情形，由于数据不完备的固有缺陷，该算法的重建的效果并不十分理想，因此需要对重建算法与扫描几何作进一步优化，以适应实际的工业或临床需求。本文基于FDK重建的两个补偿项，将锥束CT几何拓展至z向分布的双光源情形，通过减小重建点平均锥角的方法进一步抑制锥束伪影，并提出一种双光源重建的锥角加权方法，将双光源的重建结果进行融合，得到最终重建图像。仿真实验结果表明，与单光源情形相比，本文的算法可以更加有效地提高重建图像的质量，从而有望在更大锥角的CBCT重建系统中得到应用。
- FDK /
- 锥束伪影 /
- 双光源加权
Abstract:
The Feldkamp-Davis-Kress (FDK) algorithm has the advantages of a simple structure, fast calculation speed, and high reconstruction quality, and it remains the mainstream algorithm for cone-beam computed tomography (CBCT) analytical reconstruction. However, if the cone angle for the reconstructed point is too large, the reconstruction exhibits artifacts characterized by an axial density drop. Numerous methods for suppressing this artifact have been proposed, including projection weighting, cone-beam rebinning, and introducing compensation terms. The compensation method has high computational efficiency and achieves good artifact suppression when the cone angle is not more than 16°. However, for cases with larger cone angles, the effectiveness of this algorithm is diminished. Thus, further optimization of the reconstruction algorithms and scanning geometry is required to accommodate industrial and clinical demands. Based on the two compensation terms for FDK reconstruction, this study extends cone-beam CT geometrically to the case of dual source in the z-direction distribution, further suppressing cone-beam artifacts by reducing the average cone angle of the reconstructed points. A cone-angle weighting method is proposed for dual-source reconstruction, to fuse the reconstructed results of the two sources and obtain the final reconstructed image. The simulation results show that the proposed algorithm can improve the quality of the reconstructed image more effectively than single-source case.
- FDK /
- cone-beam artifact /
- dual-source weighting

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图 1 FDK算法的扫描几何关系

Figure 1. Scanning geometry of FDK algorithm

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图 2 双光源CT的扫描几何

Figure 2. Scanning geometry of dual-source CT

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图 3 圆轨道CBCT的Radon空间数据分布

Figure 3. Data distribution in Radon space of circular cone-beam computed tomography (CBCT)

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图 4 双光源CT的锥角几何

Figure 4. Cone angle geometry of dual-source CT

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图 5 双光源CT投影权重因子分布示意图

Figure 5. Weight factor distribution of dual-source CT

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图 6 本文提出的权重因子$ {w}_{1} $与$ {w}_{2} $

Figure 6. Proposed weight factors $ {w}_{1} $ and $ {w}_{2} $

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图 7 双光源CT系统的重建过程

Figure 7. Reconstruction process of dual-source CT

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图 8 Shepp-Logan体模和Defrise-Discs体模的重建结果，x-z方向，y=−7.7 mm，Shepp-Logan视窗：[0.98，1.05]，Defrise-Discs视窗：[0.7，1.1]

Figure 8. Reconstruction result of Shepp-Logan phantom and Defrise-Discs phantom, x-z views. Shepp-Logan Display window: [0.98, 1.05], Defrise-Discs display window: [0.7, 1.1]

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图 9 Shepp-Logan体模与Defrise-Discs重建结果的profile曲线

Figure 9. Profile curve of Shepp-Logan and Defrise-Discs phantoms

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表 1 本文中的双光源CT系统参数

Table 1 Parameters of the dual-source CT system in this study

参数	值
旋转半径$ R $	100 mm
源探距离$ D $	200 mm
面阵探测器高度$ {H}_{D} $	130 mm
双光源间距$ H $	20 mm
探测器单元数$ {N}_{D}^{2} $	256×256
重建体素数$ {N}_{V}^{3} $	128×128×128
重建立方体区域边长$ W $	60 mm
全扫描角度采样数$ {N}_{\theta } $	400

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