Reconstruction for Fluorescence Molecular Tomography Using Fast Iterative Shrinkage Thresholding Algorithm Based on Restart Strategy

Jiachen Gao; Sheng Zhong; Qiong Xie; Yating Yuan; Huangjian Yi

doi:10.3788/AOS240640

Acta Optica Sinica, Volume. 44, Issue 16, 1617001(2024)

Reconstruction for Fluorescence Molecular Tomography Using Fast Iterative Shrinkage Thresholding Algorithm Based on Restart Strategy

Jiachen Gao¹, Sheng Zhong¹, Qiong Xie², Yating Yuan¹, and Huangjian Yi^1、*

Author Affiliations

¹School of Information Science & Technology, Northwest University, Xi’an 710127, Shaanxi , China

²The First Hospital of Hunan University of Chinese Medicine, Changsha 410007, Hunan , China

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Figures & Tables(7)

Fig. 1. Digital mouse model

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Fig. 2. Reconstruction time of two algorithms under different numbers of excitation sources

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Fig. 3. Reconstruction results of two algorithms under different noise levels. (a)-(e) Cross-sectional views of reconstructed results by FISTA at Z=16.0 mm; (f)-(j) cross-sectional views of reconstructed results by R-FISTA at Z=16.0 mm

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Fig. 4. Error analysis of FISTA and R-FISTA under different noise levels. (a) Comparison of reconstruction LE; (b) comparison of reconstruction time

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Fig. 5. Comparison of reconstruction results. (a) Reconstruction result of R-FISTA; (b) reconstruction result of FISTA; (c) comparison of reconstruction time

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Table 1. Comparison of the basic steps between R-FISTA and FISTA

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Table 1. Comparison of the basic steps between R-FISTA and FISTA

Step

Algorithm 1: FISTA

Algorithm 2: R-FISTA

Step 0

Input: $L = L (f)$

Initialization $x_{0}$ , let $y_{1} = x_{0} \in R^{n}$ , $t_{1} = 1$

Initialization

x_{0}

, let

L_{0} > 0

θ_{k} > 0

y_{1} = x_{0}

Step k

(k≥1)

Let $L_{k} = a \times L_{k}$ , until the proximal gradient condition is satisfied:

$F [p_{L_{k}} (y_{k})] \leq Q_{L_{k}} [p_{L_{k}} (y_{k}), y_{k}]$ :

$x_{k} = p_{L} (y_{k})$ ,

Calculate and judge according to the proximal gradient condition:

① If $F [p_{L_{k}} (y_{k})] > Q_{L_{k}} [p_{L_{k}} (y_{k}), y_{k}]$ ,

let $L_{k} = (1 + θ_{k}) \times L_{k}$ and calculate:

$x_{k} = p_{L_{k}} (y_{k})$ ,

$t_{k + 1} = \{\begin{array}{l} \frac{1 + \sqrt[]{1 + 4 t_{k}^{2}}}{2}, & \frac{L_{k + 1}}{L_{k}} \geq 1 \\ \frac{1 + \sqrt[]{1 + 4 \frac{L_{k + 1}}{L_{k}} t_{k}^{2}}}{2}, & \frac{L_{k + 1}}{L_{k}} < 1 \end{array}$ ,

Step k

(k≥1)

$t_{k + 1} = \frac{1 + \sqrt[]{1 + 4 t_{k}^{2}}}{2}$ ,

$y_{k + 1} = x_{k} + (\frac{t_{k} - 1}{t_{k + 1}}) (x_{k} - x_{k - 1})$ ,

$k = k + 1$

$y_{k + 1} = x_{k} + (\frac{t_{k} - 1}{t_{k + 1}}) (x_{k} - x_{k - 1})$ .

Update $θ_{k}$ :

$θ_{k} = \{\begin{matrix} θ_{k} - α' \times d_{k}, & \begin{matrix} α' \times d_{k} < θ_{k} \end{matrix} \\ 0.5, & e l s e \end{matrix}$ .

② If $F [p_{L_{k}} (y_{k})] \leq Q_{L_{k}} [p_{L_{k}} (y_{k}), y_{k}]$ :

if $L_{k} = L_{k - 1}$ , reboot, $L_{k} = L_{0}$ ;

else $L_{k} = L_{k - 1}$ , $k = k + 1$

Table 2. Simulation experiment results

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Table 2. Simulation experiment results

Number of excitation sources	Algorithm	NRMSE	LE /mm	Time /s
4	R-FISTA	0.0120	0.840	1.70±0.04
4	FISTA	0.0150±0.003	1.000±0.13	3.78±1.10
8	R-FISTA	0.0165±0.0005	0.538±0.019	4.33±0.21
8	FISTA	0.0200±0.003	0.720±0.13	5.46±1.37
16	R-FISTA	0.0170±0.0002	0.520±0.006	9.75±0.33
16	FISTA	0.0160±0.0004	0.730±0.13	16.56±3.79
36	R-FISTA	0.0180±0.0002	0.480±0.01	32.71±2.05
36	FISTA	0.0230±0.003	0.910±0.24	42.71±14.99

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Jiachen Gao, Sheng Zhong, Qiong Xie, Yating Yuan, Huangjian Yi. Reconstruction for Fluorescence Molecular Tomography Using Fast Iterative Shrinkage Thresholding Algorithm Based on Restart Strategy[J]. Acta Optica Sinica, 2024, 44(16): 1617001

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Paper Information

Category: Medical optics and biotechnology

Received: Feb. 18, 2024

Accepted: Apr. 24, 2024

Published Online: Aug. 5, 2024

The Author Email: Yi Huangjian (yhj2014@nwu.edu.cn)

DOI:10.3788/AOS240640

CSTR:32393.14.AOS240640

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology