基于加权总差分最小化的中子稀疏投影计算机断层重建方法 
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Neutron Computed Tomography Reconstruction Method Using Sparse Projections Based on Weighted Total Difference Minimization
1 北京航空航天大学机械工程及自动化学院, 北京 100191
2 中国工程物理研究院核物理与化学研究所, 四川 绵阳 621900
图 & 表
图 1. Shepp-Logan重建图像。(a)理想图像;(b) ART算法;(c) SART算法;(d) SIRT算法
Fig. 1. Reconstructed images of Shepp-Logan. (a) Ideal image; (b) ART algorithm; (c) SART algorithm; (d) SIRT algorithm
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图 2. 含噪声投影数据下Shepp-Logan重建图像。(a)理想图像;(b) ART算法;(c) SART算法;(d) SIRT算法
Fig. 2. Reconstructed images of Shepp-Logan using noisy projections. (a) Ideal image; (b) ART algorithm; (c) SART algorithm; (d) SIRT algorithm
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图 3. 不同稀疏角度投影FBP与SIRT重建图像。(a) 180幅投影FBP重建图像;(b) 20幅投影FBP重建图像;(c) 180幅投影SIRT重建图像;(d) 20幅投影SIRT重建图像
Fig. 3. Reconstructed images obtained by FBP and SIRT with different sparse angle projections. (a) FBP reconstructed image with 180 projections; (b) FBP reconstructed image with 20 projections; (c) SIRT reconstructed image with 180 projections; (d) SIRT reconstructed image with 20 projections
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图 4. WTDM方法在不同方向的差分测度[17]。(a)像素点四邻域示意图;(b)像素点各方向的局部梯度
Fig. 4. Difference measures of WTDM method in different directions[17]. (a) Diagram of four neighbors of pixel point; (b) partial gradients of pixel point in different directions
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图 5. 90幅投影Shepp-Logan的重建图像。(a) FBP重建;(b) SIRT重建;(c) SART-WTDM重建;(d) SIRT-WTDM重建
Fig. 5. Reconstructed images of Shepp-Logan using 90 projections. (a) FBP reconstruction; (b) SIRT reconstruction; (c) SART-WTDM reconstruction; (d) SIRT-WTDM reconstruction
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图 6. 90幅含噪声投影Shepp-Logan的重建图像。(a) FBP重建;(b) SIRT重建;(c) SART-WTDM重建;(d) SIRT-WTDM重建
Fig. 6. Reconstructed images of Shepp-Logan using 90 noisy projections. (a) FBP reconstruction; (b) SIRT reconstruction; (c) SART-WTDM reconstruction; (d) SIRT-WTDM reconstruction
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图 7. Shepp-Logan的90幅投影重建图像的灰度曲线。(a)投影数据无噪声;(b)投影数据含噪声
Fig. 7. Gray curves of reconstructed images of Shepp-Logan with 90 projections. (a) Without noise in projections; (b) with noise in projections
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图 8. 编码管样品75幅投影重建图像。(a)完整数据FBP重建;(b) 75幅投影FBP重建;(c) 75幅投影SIRT重建;(d) 75幅投影SART-WTDM重建;(e) 75幅投影SIRT-WTDM重建
Fig. 8. Reconstructed images of code tube sample with 75 projections. (a) FBP reconstruction with complete projections; (b) FBP reconstruction with 75 projections; (c) SIRT reconstruction with 75 projections; (d) SART-WTDM reconstruction with 75 projections; (e) SIRT-WTDM reconstruction with 75 projections
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图 9. 编码管样品18幅投影重建图像。(a)完整数据FBP重建;(b) 18幅投影FBP重建;(c) 18幅投影SIRT重建;(d) 18幅投影SART-WTDM重建;(e) 18幅投影SIRT-WTDM重建
Fig. 9. Reconstructed images of code tube sample with 18 projections. (a) FBP reconstruction with complete projections; (b) FBP reconstruction with 18 projections; (c) SIRT reconstruction with 18 projections; (d) SART-WTDM reconstruction with 18 projections; (e) SIRT-WTDM reconstruction with 18 projections
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图 10. 编码管样品的三维可视化结果。(a)编码管样品的重建部位;(b)完整数据FBP重建;(c) 75幅投影数据FBP重建;(d) 75幅投影数据SIRT重建;(e) 75幅投影数据SART-WTDM重建;(f) 75幅投影数据SIRT-WTDM重建
Fig. 10. 3D visualization results of code tube sample. (a) Reconstructed region of code tube sample; (b) FBP reconstructed result with complete projections; (c) FBP reconstructed result with 75 projections; (d) SIRT reconstructed result with 75 projections; (e) SART-WTDM reconstructed result with 75 projections; (f) SIRT-WTDM reconstructed result with 75 projections
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表 1Shepp-Logan重建图像的MSE和PSNR
Table1. MSE and PSNR of reconstructed images of Shepp-Logan
| Method | Without noise in the projections | With noise in the projections | Image quality reduction rate | | |
|---|
| MSE | PSNR /dB | MSE | PSNR /dB | Increasing rate of MSE /% | Reduction rate of PSNR /% |
|---|
| ART | 0.0047 | 71.4516 | 0.0078 | 69.1832 | 65.96 | 3.17 | | SART | 0.0047 | 71.4208 | 0.0077 | 69.2508 | 63.83 | 3.04 | | SIRT | 0.0046 | 71.5167 | 0.0049 | 71.2571 | 6.52 | 0.36 |
|
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表 2基于Shepp-Logan模拟的CT条件
Table2. Simulative CT conditions based on Shepp-Logan
| Scanning mode | Reconstructing image size /(pixel×pixel) | Range of scanning angle /(°) | Angle step /(°) |
|---|
| Parallel beam | 256×256 | 180 | 2 |
|
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表 3Shepp-Logan的90幅投影重建图像的MSE和PSNR
Table3. MSE and PSNR of reconstructed images of Shepp-Logan with 90 projections
| Method | Without noise in projections | With noise in projections | |
|---|
| MSE | PSNR /dB | MSE | PSNR /dB |
|---|
| FBP | 0.0100 | 68.1374 | 0.0118 | 67.4080 | | SIRT | 0.0046 | 71.4593 | 0.0064 | 70.0438 | | SART-WTDM | 0.0045 | 71.5842 | 0.0062 | 70.1929 | | SIRT-WTDM | 0.0045 | 71.5850 | 0.0062 | 70.2200 |
|
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表 4编码管样品CT扫描条件
Table4. CT scanning conditions of code tube sample
| Neutron beam type | Detector type | Number of detector pixels | Range of scanning angle /(°) | Total projection number |
|---|
| Cold neutron | Andor iKon-L 936 | 2048×2048 | 180 | 450 |
|
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表 5编码管样品重建图像的MSE和PSNR
Table5. MSE and PSNR of reconstructed images of code tube sample
| Method | 776th slice image | 313rd slice image | |
|---|
| MSE | PSNR /dB | MSE | PSNR /dB |
|---|
| FBP | 9.8263×10-4 | 78.2069 | 0.0131 | 66.9626 | | SIRT | 9.4837×10-4 | 78.3610 | 0.0090 | 68.6035 | | SART-WTDM | 7.6070×10-4 | 79.3187 | 0.0042 | 71.8748 | | SIRT-WTDM | 4.0869×10-4 | 82.0169 | 0.0037 | 72.4440 |
|
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林强, 杨民, 唐彬, 刘斌, 霍合勇, 刘家伟. 基于加权总差分最小化的中子稀疏投影计算机断层重建方法[J]. 光学学报, 2019, 39(7): 0711003. Qiang Lin, Min Yang, Bin Tang, Bin Liu, Heyong Huo, Jiawei Liu. Neutron Computed Tomography Reconstruction Method Using Sparse Projections Based on Weighted Total Difference Minimization[J]. Acta Optica Sinica, 2019, 39(7): 0711003.
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