Sparse Angle CT Image Reconstruction Algorithm Based on Multi-Directional Total Variation

Kunran Yi; Han Wang; Daohua Zhan; Zhuohao Shi; Yibin Chen; Feiyu Fang

doi:10.3788/LOP241627

Laser & Optoelectronics Progress, Volume. 62, Issue 6, 0611002(2025)

Sparse Angle CT Image Reconstruction Algorithm Based on Multi-Directional Total Variation

Kunran Yi¹, Han Wang^1、*, Daohua Zhan¹, Zhuohao Shi¹, Yibin Chen¹, and Feiyu Fang²

Author Affiliations

¹School of Electromechanical Engineering, Guangdong University of Technology, Guangzhou 510006, Guangdong , China

²School of Advanced Manufacturing Technology, Guangdong Mechanical ＆ Electrical Polytechnic, Guangzhou 510515, Guangdong , China

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Figures & Tables(7)

Fig. 1. Schematic of directional gradient difference operator

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Fig. 2. Reconstructed image of Shepp-Logan phantom model,grayscale range is [0,1].(a) Original image; (b) ART algorithm; (c) ATV algorithm; (d) POCS-TVM algorithm; (e) MDTV algorithm

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Fig. 3. Horizontal and vertical contour curves of reconstructed image with Shepp-Logan phantom model. (a) Horizontal contour curve; (b) horizontal local zoomed-in contour curve; (c) vertical contour curve; (d) vertical local zoomed-in contour curve

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Fig. 4. Reconstructed image of gear CT,grayscale range is [0,1].(a) Reference image; (b) ART algorithm; (c) ATV algorithm; (d) POCS-TVM algorithm; (e) MDTV algorithm

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Table 0. [in Chinese]

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Table 0. [in Chinese]

输入：投影数据

P

，外循环总迭代次数

K

，正则化迭代次数

T

，松弛因子

λ

，调节因子

α

，修正因子

α_{r}

，比例因子

r

1：初始化： $f^{0} \leftarrow 0$

2：外循环：For $k = 1 : K$

3：ART算法迭代： $f_{A R T}^{k} = f_{A R T}^{k - 1} + λ \frac{(p_{i} - A_{i} f_{A R T}^{k - 1}) A_{i}^{T}}{‖ A_{i} ‖^{2}}$

4：非负约束： $f_{P O S}^{k} = \{\begin{matrix} f_{A R T}^{k}, f_{A R T}^{k} \geq 0 \\ 0, f_{A R T}^{k} < 0 \end{matrix}$

5：初始化： $f_{M D T V}^{k, 0} \leftarrow f_{P O S}^{k}$

6：增量因子： $\nabla f_{P O S} = |f_{A R T}^{k} - f_{P O S}^{k}|$

7：内循环：For $t = 1 : T$

8：计算梯度下降方向： $G_{i, j} = \frac{\partial {‖f‖}_{M D T V}}{\partial f_{i, j}}$ ， ${\hat{G}}_{i, j} = \frac{G_{i, j}}{‖G_{i, j}‖}$

9：MDTV算法迭代： $f_{M D T V}^{k, t} = f_{M D T V}^{k, t - 1} - α \nabla f_{P O S} {\hat{G}}_{i, j}$

10：若满足 $t = T$ ，结束内循环， $f_{A R T}^{k} \leftarrow f_{M D T V}^{k, T}$

11：增量因子： $\nabla f_{M D T V} = |f_{M D T V}^{k} - f_{P O S}^{k}|$

12：调节因子修正： $α = \{\begin{matrix} α \cdot α_{r}, & \nabla f_{M D T V} \geq r \cdot \nabla f_{P O S} \\ α & o t h e r s \end{matrix}$

13：若满足 $k = K$ ，结束外循环， $f^{K} \leftarrow f_{A R T}^{k}$

14：输出： $f^{K}$

Table 1. Image reconstruction quality evaluation metrics of Shepp-Logan phantom model
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Table 1. Image reconstruction quality evaluation metrics of Shepp-Logan phantom model
Parameter ART ATV POCS-TVM MDTV
PSNR /dB 25.7657 35.0184 37.9008 39.3717
SSIM 0.8199 0.8869 0.9497 0.9677
RMSE 0.0513 0.0177 0.0127 0.0107

Table 2. Reconstruction quality performance metrics of gear CT images
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Table 2. Reconstruction quality performance metrics of gear CT images
Parameter ART ATV POCS-TVM MDTV
PSNR /dB 23.9119 28.9877 33.2910 35.5284
SSIM 0.6373 0.7543 0.8726 0.9140
RMSE 0.0634 0.0354 0.0216 0.0167

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Kunran Yi, Han Wang, Daohua Zhan, Zhuohao Shi, Yibin Chen, Feiyu Fang. Sparse Angle CT Image Reconstruction Algorithm Based on Multi-Directional Total Variation[J]. Laser & Optoelectronics Progress, 2025, 62(6): 0611002

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