Three-term conjugate gradient method for X-ray luminescence computed tomography

Yuqing Hou; Yuqing Hou; Zijian Tang; Zijian Tang; Huangjian Yi; Huangjian Yi; Hongbo Guo; Hongbo Guo; Jingjing Yu; Xiaowei He; Xiaowei He; Xiaowei He

doi:10.1364/JOSAA.423149

Journal of the Optical Society of America A
Vol. 38,
Issue 7,
pp. 985-991
(2021)
•https://doi.org/10.1364/JOSAA.423149

Three-term conjugate gradient method for X-ray luminescence computed tomography

Yuqing Hou, Zijian Tang, Huangjian Yi, Hongbo Guo, Jingjing Yu, and Xiaowei He

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
Yuqing Hou, Zijian Tang, Huangjian Yi, Hongbo Guo, Jingjing Yu, and Xiaowei He, "Three-term conjugate gradient method for X-ray luminescence computed tomography," J. Opt. Soc. Am. A 38, 985-991 (2021)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Citation alert
Save article
Editors' Pick

Check for updates

Abstract

X-ray luminescence computed tomography (XLCT) has become an emerging hybrid molecular imaging technology with high detection sensitivity and low cost. However, the inverse problem of reconstruction has severe ill-posed consequences. The original regularization algorithm needs to take much time to solve the problem. To reduce the cost of time, a three-term conjugate gradient (TTCG) algorithm is proposed for XLCT. Useful truncation information is added to the descent direction to find the optimal solution quickly in our proposed algorithm. Both numerical simulation experiments and real experiments are carried out to verify the performance of the algorithm. Experimental results show that the presented algorithm can effectively speed up the reconstruction process.

Full Article | PDF Article

More Like This

Regularized reconstruction based on joint L₁ and total variation for sparse-view cone-beam X-ray luminescence computed tomography

Tianshuai Liu, Junyan Rong, Peng Gao, Huangsheng Pu, Wenli Zhang, Xiaofeng Zhang, Zhengrong Liang, and Hongbing Lu
Biomed. Opt. Express 10(1) 1-17 (2019)

Sparse reconstruction based on dictionary learning and group structure strategy for cone-beam X-ray luminescence computed tomography

Yi Chen, Mengfei Du, Gege Zhang, Jun Zhang, Kang Li, Linzhi Su, Fengjun Zhao, Huangjian Yi, and Xin Cao
Opt. Express 31(15) 24845-24861 (2023)

X-ray luminescence computed tomography imaging based on X-ray distribution model and adaptively split Bregman method

Dongmei Chen, Shouping Zhu, Xu Cao, Fengjun Zhao, and Jimin Liang
Biomed. Opt. Express 6(7) 2649-2663 (2015)

Previous Article Next Article

Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (6)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Tables (7)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (15)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Organ	Muscle	Heart	Stomach	Liver	Kidney	Lung
Absorption coefficient $({m m}^{- 1})$	0.204	0.138	0.026	0.829	0.155	0.459
Reduced scattering coefficient $({m m}^{- 1})$	0.534	1.077	1.549	0.736	2.533	2.265

Algorithm	Iteration Number	Time (s)	Location Error (mm)	NRMSE
IVTCG	115	42.2	0.45	0.042
TTCG	63	23.5	0.45	0.040

Algorithm	Iteration Number	Time(s)	Location Error (mm)	NRMSE
IVTCG	45	16.5	0.96	0.108
TTCG	45	15.7	0.71	0.090

			Location Error (mm)		NRMSE
Algorithm	Iteration Number	Time(s)	Target 1	Target 2	Target 1	Target 2
IVTCG	483	384.8	0.70	0.50	0.102	0.061
TTCG	426	316.1	0.70	0.49	0.102	0.061

			Location Error (mm)		NRMSE
Algorithm	Iteration Number	Time(s)	Target 1	Target 2	Target 1	Target 2
IVTCG	395	299.3	0.66	3.43	0.102	0.071
TTCG	395	290.4	0.66	0.51	0.100	0.060

Algorithm: The three-term conjugate gradient method
Step 0: Parameter initialization. Set $x_{0} = 0, \nabla F (x_{0}) = b, d_{0} = - \nabla F (x_{0})$ and $ε \geq 0$ . Then set iteration parameters $t = 0, k = 0$ and maximum number of iterations ${i t e r}_{m a x}$ .
Step 1: If $‖ \nabla F (x_{k}) ‖_{2}^{2} \leq ε$ or $t > {i t e r}_{m a x}$ , turn to step 7, else set $α_{k} = \frac{‖ \nabla F (x_{k}) ‖_{2}^{2}}{d_{k}^{T} B d_{k}}$ .
Step 2 : Set $x_{k + 1} = x_{k} + α_{k} d_{k}, k = k + 1.$ If $‖ \nabla F (x_{k}) ‖_{2}^{2} \leq ε$ , then turn to step 7, else turn to step 3.
Step 3 : If $z_{I_{k}}^{k} + x_{k} + α_{k} d_{k} \geq 0,$ set $x_{k + 1} = x_{k} + α_{k} d_{k},$ else turn to step 6.
Step 4 : Check $\| g_{k - 1}^{T} g_{k} \| \geq 0.2 ‖ g_{k} ‖^{2}, - 1.2 ‖ g_{k} ‖^{2} > d_{k}^{T} g_{k}, d_{k}^{T} g_{k} > - 0.8 ‖ g_{k} ‖^{2}$ , If the condition is true set $t = k - 1$ and go to step 5, or go straight to step 5.
Step 5 : Set $β_{k - 1} = \frac{g_{k}^{T} (g_{k} - g_{k - 1})}{d_{k - 1}^{T} (g_{k} - g_{k - 1})}, γ_{k - 1} = {\begin{matrix} 0 & w h e n \dots t = k - 1 \\ \frac{g_{k}^{T} (g_{t + 1} - g_{t})}{d_{t}^{T} (g_{t + 1} - g_{t})} & w h e n \dots t < k - 1 \end{matrix}$ $d_{k} = - g_{k} + β_{k - 1} d_{k - 1} + γ_{k - 1} d_{t}, k = k + 1$ . Then turn to step 1, else go to step 6.
Step 6 : Compute the largest non-negative scalar $α^{}$ that satisfies $z_{I_{k}}^{k} + x_{k} + α_{k} d_{k} \geq 0$ , set $x_{k + 1} = x_{k} + α^{} d_{k},$ turn to step 7.
Step 7 : Set $d_{I_{k}}^{k} = x_{k + 1}$ .

Algorithm: The three-term conjugate gradient method
Step 0: Parameter initialization. Set $x_{0} = 0, \nabla F (x_{0}) = b, d_{0} = - \nabla F (x_{0})$ and $ε \geq 0$ . Then set iteration parameters $t = 0, k = 0$ and maximum number of iterations ${i t e r}_{m a x}$ .
Step 1: If $‖ \nabla F (x_{k}) ‖_{2}^{2} \leq ε$ or $t > {i t e r}_{m a x}$ , turn to step 7, else set $α_{k} = \frac{‖ \nabla F (x_{k}) ‖_{2}^{2}}{d_{k}^{T} B d_{k}}$ .
Step 2 : Set $x_{k + 1} = x_{k} + α_{k} d_{k}, k = k + 1.$ If $‖ \nabla F (x_{k}) ‖_{2}^{2} \leq ε$ , then turn to step 7, else turn to step 3.
Step 3 : If $z_{I_{k}}^{k} + x_{k} + α_{k} d_{k} \geq 0,$ set $x_{k + 1} = x_{k} + α_{k} d_{k},$ else turn to step 6.
Step 4 : Check $\| g_{k - 1}^{T} g_{k} \| \geq 0.2 ‖ g_{k} ‖^{2}, - 1.2 ‖ g_{k} ‖^{2} > d_{k}^{T} g_{k}, d_{k}^{T} g_{k} > - 0.8 ‖ g_{k} ‖^{2}$ , If the condition is true set $t = k - 1$ and go to step 5, or go straight to step 5.
Step 5 : Set $β_{k - 1} = \frac{g_{k}^{T} (g_{k} - g_{k - 1})}{d_{k - 1}^{T} (g_{k} - g_{k - 1})}, γ_{k - 1} = {\begin{matrix} 0 & w h e n \dots t = k - 1 \\ \frac{g_{k}^{T} (g_{t + 1} - g_{t})}{d_{t}^{T} (g_{t + 1} - g_{t})} & w h e n \dots t < k - 1 \end{matrix}$ $d_{k} = - g_{k} + β_{k - 1} d_{k - 1} + γ_{k - 1} d_{t}, k = k + 1$ . Then turn to step 1, else go to step 6.
Step 6 : Compute the largest non-negative scalar $α^{}$ that satisfies $z_{I_{k}}^{k} + x_{k} + α_{k} d_{k} \geq 0$ , set $x_{k + 1} = x_{k} + α^{} d_{k},$ turn to step 7.
Step 7 : Set $d_{I_{k}}^{k} = x_{k + 1}$ .

Abstract

Data Availability

Cited By

Figures (6)

Tables (7)

Equations (15)

Journal of the Optical Society of America A