Gradient Domain Point Spread Function Estimation and Blind Restoration of Adaptive Optical System Images

Huanyu Xu; Mengxi Xu; Yu She; Lifa Hu; Li Xuan

doi:10.3788/LOP212528

Laser & Optoelectronics Progress, Volume. 60, Issue 4, 0401001(2023)

Gradient Domain Point Spread Function Estimation and Blind Restoration of Adaptive Optical System Images

Huanyu Xu^1、*, Mengxi Xu¹, Yu She², Lifa Hu³, and Li Xuan⁴

Author Affiliations

¹School of IOT, Wuxi University, Wuxi 214105, Jiangsu, China

²School of Automation, Nanjing University of Information Science & Technology, Nanjing 210044, Jiangsu, China

³School of Science, Jiangnan University, Wuxi 214122, Jiangsu, China

⁴State Key Laboratory of Applied Optics, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, Jilin, China

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Figures & Tables(15)

Fig. 1. Flow chart of proposed algorithm

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Fig. 2. Original object images and different noise level degraded images. (a) Original object; (b) k=1000 degraded image; (c) k=100 degraded image; (d) k=40 degraded image

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Fig. 3. Reconstruction images of different algorithms for k=1000. (a) Framelet based algorithm; (b) OBD algorithm; (c) proposed algorithm

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Fig. 4. Reconstruction images of different algorithms for k=100. (a) Framelet based algorithm; (b) OBD algorithm; (c) proposed algorithm.

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Fig. 5. Reconstruction images of different algorithms for k=40. (a) Framelet based algorithm; (b) OBD algorithm; (c) proposed algorithm

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Fig. 6. Reconstruction PSF for different methods. (a) Original PSF; (b) PSF obtained by Framelet based algorithm; (c) PSF obtained by OBD algorithm; (d) PSF obtained by proposed algorithm

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Fig. 7. Schematic diagram of LC-AO imaging system

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Fig. 8. Optical layout of LC-AO imaging system

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Fig. 9. Acquired and reconstruction images of a star. (a) Acquired image; (b) reconstruction image by OBD algorithm; (c) reconstruction image by proposed algorithm

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Fig. 10. Full width at half maximum for different images in Fig. 9

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Fig. 11. Acquired and reconstruction images of the COSMOS1461 satellite. (a) Acquired image; (b) reconstruction image by OBD algorithm; (c) reconstruction image by proposed algorithm

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Fig. 12. Experimental result of binary star imaging observation

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Table 1. Procedure of proposed point spread function estimation algorithm

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Table 1. Procedure of proposed point spread function estimation algorithm

Algorithm 1

Apply gradient filter to $g$ ，obtain high frequency degenerated image $y$

For k=1，2，3，…

Update $x^{k}$ using equation（10）

Update $h^{k}$ using equation（11）

End

Return point spread function $h$ after the last iteration

Input：degenerated image $g$ ，size of point spread function $s_{h}$

Output：point spread function $h$

Table 2. Procedure of proposed image restoration algorithm

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Table 2. Procedure of proposed image restoration algorithm

Algorithm 2

Acquire point spread function $h$ from $g$ using Algorithm 1

For i=1，2，3…

$u_{i + 1} = u_{i} (h^{T} * \frac{g}{h * u_{i}})$

Apply low filter $f_{l}$ to $u_{i + 1}$ ，acquire updated restored image $u_{i + 1}$

End

Return $u$ after the last iteration

Input：degenerated image $g$ ，size of point spread function $s_{h}$

Output：restored image $u$

Table 3. RMSE and SSIM results of simulated image experiments
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Table 3. RMSE and SSIM results of simulated image experiments
k Framelet OBD Proposed algorithm
RMSE SSIM RMSE SSIM RMSE SSIM
1000 0.0841 0.855 0.290 0.800 0.0406 0.905
100 0.0750 0.867 0.313 0.788 0.0452 0.906
40 0.0890 0.848 0.340 0.792 0.0849 0.889

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Huanyu Xu, Mengxi Xu, Yu She, Lifa Hu, Li Xuan. Gradient Domain Point Spread Function Estimation and Blind Restoration of Adaptive Optical System Images[J]. Laser & Optoelectronics Progress, 2023, 60(4): 0401001

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