Fringe Reconstruction Technology of Two-Dimensional Shock Wave Velocity Field Based on Total Variation Regularization Constraints

Fig. 3. Fringe patterns reconstructed by TVAL3H algorithm. (a) 25 frame reconstruction 1×1; (b) 50 frame reconstruction 1×1; (c) 100 frame reconstruction 1×1; (d) 150 frame reconstruction 1×1; (e) 25 frame reconstruction 7×7; (f) 50 frame reconstruction 7×7; (g) 100 frame reconstruction 7×7; (h) 150 frame reconstruction 7×7

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Fig. 4. Velocity fringe restoration images of shock wave diagnosis by different algorithms. (a) TVAL3 algorithm; (b) TVAL3H algorithm; (c) GAP algorithm; (d) ADMM algorithm

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Fig. 5. Reconstruction performance indices of different algorithms under 7×7 coding aperture. (a) PSNRs of different algorithms; (b) SSIMs of different algorithms

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Fig. 6. Comparison of reconstruction speed of different algorithms under 7×7 coding aperture

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Fig. 7. Comparison of recovery performance of different algorithms at the same time order. (a) PSNRs of different algorithms; (b) SSIMs of different algorithms

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Table 1. Flow chart of TVAL3H algorithm

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Table 1. Flow chart of TVAL3H algorithm

Input：coding matrix $A$ ，measurement matrix $y$ ，maximum iterations maxcnt；
Output：reconstruct data $x$ ；
Initialization： $w$ ， $x$ ， $v$ ， $β$ ， $λ$ ， $μ$ ；
1）The problem to be solved is divided into two subproblems by method of the augmented Lagrange function；
2）Substitute $x$ into subproblem 1，and solve $w_{i}$ using iterative shrinkage；
3）Substitute $w_{i}$ into subproblem 2，and $x$ is solved using Barzilai-Borwein gradient method；
4）Update Lagrange multiplier $v$ ， $λ$ ，and update penalty function factor $β$ ， $μ$ ；
5）Step 2）and step 3）alternate iteration，and stop iteration when accuracy meets the requirements or iterations reach maximum number.

Table 2. Diagnosis of fringe reconstruction results using TVAL3H reconstruction algorithm under different frame number conditions

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Table 2. Diagnosis of fringe reconstruction results using TVAL3H reconstruction algorithm under different frame number conditions

Aperture	Performance	25 frame	50 frame	100 frame	150 frame
1×1	PSNR /dB	26.71	24.07	19.36	18.39
	SSIM /%	90.02	87.38	79.63	76.96
	Time /s	155	396	1321	2613
7×7	PSNR /dB	17.14	12.87	11.61	10.81
	SSIM /%	74.18	58.66	53.09	49.91
	Time /s	158	395	1379	2490

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Miao Li, Baishan Yu, Xi Wang, Lei Zhang, Chenyan Wang, Jiaxin Liang. Fringe Reconstruction Technology of Two-Dimensional Shock Wave Velocity Field Based on Total Variation Regularization Constraints[J]. Acta Optica Sinica, 2023, 43(19): 1911003

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Paper Information

Category: Imaging Systems

Received: Feb. 20, 2023

Accepted: Apr. 23, 2023

Published Online: Oct. 23, 2023

The Author Email: Xi Wang (xiwang@cqupt.edu.cn)

DOI:10.3788/AOS230777

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology