Five-view three-dimensional reconstruction for ultrafast dynamic imaging of pulsed radiation sources

Jianpeng Gao; Liang Sheng; Xinyi Wang; Yanhong Zhang; Liang Li; Baojun Duan; Mei Zhang; Yang Li; Dongwei Hei

doi:10.1063/5.0177342

Matter and Radiation at Extremes, Volume. 9, Issue 2, 027801(2024)

Five-view three-dimensional reconstruction for ultrafast dynamic imaging of pulsed radiation sources

Jianpeng Gao1...2,*, Liang Sheng2, Xinyi Wang2, Yanhong Zhang2, Liang Li1, Baojun Duan2, Mei Zhang2, Yang Li2 and Dongwei Hei2 |Show fewer author(s)

Author Affiliations

¹Department of Engineering Physics, Tsinghua University, Beijing 100084, China

²National Key Laboratory of Intense Pulsed Radiation Simulation and Effect, Northwest Institute of Nuclear Technology, Xi’an 710024, China

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Figures & Tables(14)

Fig. 1. Structure of neural network.

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Fig. 2. The angular distribution of the imaging axes: 1, (90°,180°); 2, (90°,135°); 3, (90°,90°); 4, (90°,45°); 5, (90°,22.5°).

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Fig. 3. 3D reconstructed results of three different algorithms. (a1)–(a3) Perspective view, 3D view and slice image at x = 0 of simulated data, respectively. (b1)–(b3) Results of analytical method. (c1)–(c3) Results of iterative method. (d1)–(d3) Results of DIP processing.

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Fig. 4. 3D reconstructed results of three different algorithms with noisy data. (a1)–(a3) Perspective view, 3D view, and slice image at x = 0 of analytical results, respectively. (b1)–(b3) Results of iterative method. (c1)–(c3) Results of DIP processing.

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Fig. 5. Comparison between projections of reconstruction results and simulation data projections. (a1) Projection of simulation data at angle 1. (a2) Projection with noise. (b1) and (b2) Difference images between simulation data projection and projection of analytical results with and without noisy data. (c1) and (c2) Difference projection images of iterative results with and without noisy data. (d1) and (d2) Difference projection images of iteration with DIP results with and without noisy data.

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Fig. 6. Convergence curve of iterative process (a) and loss curve of DIP (b) with and without noisy data.

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Fig. 7. Schematic of XUV/SR pinhole imaging system.⁶

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Fig. 8. (a) Raw projection data and (b)–(e) preprocessed images of angle 1 from shot 2 023 052 405.

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Fig. 9. 3D spatial distributions of XUV/SR emission reconstructed by analytical method. (a1)–(a4) Reconstructed 3D images from shot 2 023 052 405 at T₁, …, T₄, respectively. (b1)–(b4) Perspective images from shot 2 023 052 405 at T₁, …, T₄, respectively. (c1)–(c4) Reconstructed 3D images from shot 2 023 052 406 at T₁, …, T₄, respectively. (d1)–(d4) Perspective images from shot 2 023 052 406 at T₁, …, T₄, respectively.

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Fig. 10. 3D spatial distributions of XUV/SR emission reconstructed by the iterative method with DIP. (a1)–(a4) Reconstructed 3D images from shot 2 023 052 405 at T₁, …, T₄, respectively. (b1)–(b4) Perspective images from shot 2 023 052 405 at T₁, …, T₄, respectively. (c1)–(c4) Reconstructed 3D images from shot 2 023 052 406 at T₁, …, T₄, respectively. (d1)–(d4) Perspective images from shot 2 023 052 406 at T₁, …, T₄, respectively.

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Fig. 11. Slice images of XUV/SR emission reconstructed by the iterative method with DIP. (a1)–(a4) XUV/SR emission slice images at z = −47 from shot 2 023 052 405 at T₁, …, T₄, respectively. (b1)–(b4) XUV/SR emission slice images at z = 113 from shot 2 023 052 405 at T₁, …, T₄, respectively.

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Table 1. Iterative method using cylindrical harmonic decomposition.

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Table 1. Iterative method using cylindrical harmonic decomposition.

Parameters: M, maximum expansion order; K, iteration number; ɛ, difference between the projection images of the results in two adjacent iterations; λ, μ₀, d₀, b₀, parameters of ADMM algorithm; γ, η, adaptive updating parameters.

1: Calculate s_m by analytical algorithm, t ← 0, s⁽⁰⁾ ←s_m.

2: Compute $S^{(0)} (r)$ , $I_{rec}^{(0)} \leftarrow P_{\hat{p}} \{S^{(0)}\}$ .

3: for k = 1, …, K do

4: t ← t + 1

5: for n_z = 1: N_z do

6: Obtain s^(t) by L-BFGS algorithm.

7: Compute $S^{(t)} (z)$ , set $S^{(t)} (z_{j}) = 0$ if $S^{(t)} (z_{j}) < 0$ .

8: $d_{t} \leftarrow s h r i n k (φ (s^{(t)}) + b_{t - 1}, \frac{1}{μ_{t - 1}})$

9: $b_{t} \leftarrow b_{t - 1} + φ (s^{(t)}) - d_{t}$

10: Update μ_t

11: end for

12: if $\frac{1}{N_{x} N_{y}} I_{rec}^{(t)} - I_{rec 2}^{(t - 1) 2} \leq ε$ , break;

13: end for

Table 1. Image assessment indices of sources reconstructed by the analytical method (AM), the iterative method (IM), and iteration with DIP (IM+DIP). Boldface denotes that the image assessment index of corresponding algorithm is better than that of other algorithms.

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Table 1. Image assessment indices of sources reconstructed by the analytical method (AM), the iterative method (IM), and iteration with DIP (IM+DIP). Boldface denotes that the image assessment index of corresponding algorithm is better than that of other algorithms.

	Algorithm	SSIM	PSNR	RMSE(S)	RMSE(I)
Without noise	AM	0.811 15	27.596	0.041 71	7.7679
	IM	0.955 87	39.872	0.010 15	1.0324
	IM+DIP	0.979 49	42.454	0.007 54	0.2957
With noise	AM	0.750 02	26.971	0.044 82	8.1900
	IM	0.828 43	32.365	0.024 09	2.3296
	IM+DIP	0.955 21	39.607	0.010 46	0.5068

Table 2. Artifact reduction via deep image prior.

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Table 2. Artifact reduction via deep image prior.

Parameters: σ, standard deviation of Gaussian noise; K_e, epochs;

l_r, learning rate

1 η ∼ U(0, 0.1):

2: for t = 1, …, K_e do

3: ξ ∼N(0, σ) η ←η + ξ,

4: calculate loss L_t

5: update Θ using Adam

6: end for

7: $S \leftarrow f_{Θ} (η)$

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Jianpeng Gao, Liang Sheng, Xinyi Wang, Yanhong Zhang, Liang Li, Baojun Duan, Mei Zhang, Yang Li, Dongwei Hei. Five-view three-dimensional reconstruction for ultrafast dynamic imaging of pulsed radiation sources[J]. Matter and Radiation at Extremes, 2024, 9(2): 027801

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