基于加权全变差最小化的中子外部CT重建算法

林强; 杨民; 张晓敏; 唐彬; 刘斌

doi:10.13700/j.bh.1001-5965.2020.0126

基于加权全变差最小化的中子外部CT重建算法

doi: 10.13700/j.bh.1001-5965.2020.0126

林强¹,
杨民^1, ,,
张晓敏¹,
唐彬²,
刘斌²

1.
北京航空航天大学机械工程及自动化学院, 北京 100083
2.
中国工程物理研究院核物理与化学研究所, 绵阳 621900

基金项目:

国家自然科学基金 11675012

国家自然科学基金 U1730116

核安全项目 41426020401

详细信息

通讯作者:
杨民, E-mail: minyang.ndt@buaa.edu.cn

中图分类号: TP391.4
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- 被引次数: 0
出版历程
- 收稿日期: 2020-04-07
- 录用日期: 2020-07-03
- 网络出版日期: 2021-06-20

Neutron exterior CT reconstruction algorithm based on weighted total variation minimization

1.
School of Mechanical Engineering and Automation, Beihang University, Beijing 100083, China
2.
Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, Mianyang 621900, China

Funds:

National Natural Science Foundation of China 11675012

National Natural Science Foundation of China U1730116

Nuclear Safety Project 41426020401

More Information

Corresponding author: YANG Min, E-mail: minyang.ndt@buaa.edu.cn

摘要

摘要:
针对中子外部CT检测需求，提出了基于加权方向全变差（WDTV）最小化的中子外部CT重建算法。首先，利用平行束数据对称性原理将正弦图中旋转中心另一侧缺失的投影数据进行补充；其次，采用传统FBP算法进行了外部CT扫描模式下的CT重建。为了抑制传统FBP、SART算法重建图像中径向边缘伪影，采用WDTV算法计算沿径向和周向方向的局部方向差分并作加权和。另外，在重建模型的WDTV项中引入2个权重参数以控制径向边缘和切向边缘的不同响应强度。最后，采用所提算法研究了重建图像质量与投影数据量的关系。计算机仿真和真实冷中子实验表明：基于WDTV最小化的中子外部CT重建算法能够有效抑制径向边缘伪影，获得高质量重建图像。
- 成像系统 /
- 中子断层成像 /
- 外部CT扫描 /
- 加权方向全变差(WDTV) /
- 迭代重建
Abstract:
Aimed at the requirements of the exterior CT inspection using neutron beam, an exterior CT reconstruction algorithm based on Weighted Directional Total Variation (WDTV) minimization is proposed. We first use the symmetry principle of parallel beam data to supplement the missing projection data that are on the other side of the rotation center in the sinogram. Then the FBP algorithm is used for the reconstruction under the exterior CT scanning. In order to reduce artifacts along the radial direction in the images reconstructed by the conventional FBP and SART algorithms, we choose radial direction and angular direction to calculate the local directional difference in the WDTV algorithm and then calculate the weighted sum of these two directional differences. In addition, we introduce two weight parameters into the WDTV reconstruction model to control the different edge responses' strength along radial edges and tangential edges. The relationship between the quality of reconstructed images and the amount of projection data is studied by using the proposed reconstruction algorithm. Computer simulation and real cold neutron experiments indicate that the proposed reconstruction algorithm can effectively suppress the image artifacts along the radial direction and thus high-quality reconstruction images can be obtained.
- imaging systems /
- neutron computed tomography /
- exterior CT scanning /
- Weighted Directional Total Variation (WDTV) /
- iterative reconstruction

HTML全文

图 1 中子外部CT扫描原理

Figure 1. Principle of neutron exterior CT scanning

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图 2 外部CT扫描模体

Figure 2. Sample of exterior CT scanning

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图 3 模体外部CT扫描示意

Figure 3. Schematic diagram of exterior CT scanning of sample

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图 4 模体FBP算法重建图像

Figure 4. Reconstruction image of sample by FBP algorithm

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图 5 局部方向差分计算方法^[23]

Figure 5. Calculation method of local directional difference^[23]

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图 6 探测器宽度为128时不同算法重建结果

Figure 6. Reconstruction results from different algorithms when detector width is 128

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图 7 不同探测器宽度外部CT扫描示意图

Figure 7. Schematic diagram of exterior CT scanning with different detector width

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图 8 不同探测器宽度时SART-WDTV算法重建图像

Figure 8. Images reconstructed by SART-WDTV algorithm with different detector width

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图 9 不同探测器宽度重建图像的MSE和PSNR

Figure 9. MSE and PSNR of reconstruction images with different detector width

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图 10 齿轮样品投影正弦图与SART-TV算法重建图像

Figure 10. Complete projection sinogram and SART-TV algorithm reconstruction image of gear sample

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图 11 正弦图宽度为200时FBP算法与SART算法重建图像

Figure 11. Images reconstructed by FBP and SART algorithms when sinogram width is 200

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图 12 正弦图宽度为200时SART-TV算法与SART-WDTV算法重建图像

Figure 12. Images reconstructed by SART-TV and SART-WDTV algorithms when sinogram width is 200

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图 13 正弦图宽度为122时FBP算法与SART算法重建图像

Figure 13. Images reconstructed by FBP and SART algorithms when sinogram width is 122

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图 14 正弦图宽度为122时SART-TV算法与SART-WDTV算法重建图像

Figure 14. Images reconstructed by SART-TV and SART-WDTV algorithms when sinogram width is 122

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表 1 外部CT扫描参数

Table 1. Parameters of exterior CT scanning

CT模式	探元尺寸	像素数量	角度范围	投影数量	模体大小
平行束	1像素	128像素	0°~360°	720	512像素×512像素

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表 2 模体外部CT重建图像的MSE和PSNR

Table 2. MSE and PSNR of exterior CT reconstruction images of sample

重建算法	MSE	PSNR
FBP	3 050.040	13.287 7
SART	1 319.476	16.926 8
SART-TV	1 034.756	17.982 4
SART-WDTV	874.629 8	18.712 6

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表 3 样品外部CT重建图像的MSE和PSNR

Table 3. MSE and PSNR of exterior CT reconstruction images of sample

重建算法	正弦图宽度200		正弦图宽度122
重建算法	MSE	PSNR	MSE	PSNR
FBP	1 048.667	17.924 4	1 438.552	16.551 5
SART	762.909	19.306 1	1 436.950	16.556 4
SART-TV	499.984	21.141 2	925.194	18.468 5
SART-WDTV	431.721	21.778 8	923.005	18.478 8

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