示踪粒子光学退化图像非盲复原方法
收稿日期: 2025-11-26
修回日期: 2026-01-06
录用日期: 2026-04-03
网络出版日期: 2026-04-20
基金资助
国家自然科学基金(12572320);国家自然科学基金(12102028);国家重点研发计划(2024YFA1612300);中央高校基本科研业务费专项资金
A novel approach for non-blind restoration of optically degraded images of tracer particles
Received date: 2025-11-26
Revised date: 2026-01-06
Accepted date: 2026-04-03
Online published: 2026-04-20
Supported by
National Natural Science Foundation of China(12572320);National Key Research and Development Program of China(2024YFA1612300);Fundamental Research Funds for the Central Universities
基于示踪粒子成像的速度场测量技术在流场诊断中应用广泛，但在复杂流场环境中面临气动光学效应的干扰。例如，在燃烧、超/高超声速环境下，空间分布剧烈变化的折射率场导致强烈的气动光学效应，使得示踪粒子图像严重退化进而降低速度测量的准确性。为缓解该问题，提出一种通过点扩散函数（PSF）奇异值分解（SVD）实现图像退化非盲复原的技术路径，该方法首先对视场内多个标定位置上的点扩散函数进行奇异值分解，然后采用少数空间模态和相应的空间权重系数高效重构全场点扩散函数；进一步，采用总变分（TV）正则化的理查森-露西去卷积迭代算法，并利用重构的局部点扩散函数对退化粒子图像进行非盲复原。通过系统的数值模拟实验，全面研究奇异值分解模态数量以及图像噪声水平对复原效果的影响，并针对复原性能与经典图像复原算法进行对比分析。结果表明：所提出的方法在处理稀疏粒子图像时效果显著，能够有效恢复退化模糊的粒子形态，显著提升图像的峰值信噪比（PSNR）和结构相似性衡量指数（SSIM），为基于示踪粒子图像的速度场测量技术在恶劣光学环境下的应用提供新思路。
伍环 , 王蔚然 , 熊渊 , 潘翀 , 王晋军 . 示踪粒子光学退化图像非盲复原方法[J]. 航空学报, 2026 , 47(16) : 133145 -133145 . DOI: 10.7527/S1000-6893.2026.33145
Velocity field measurement techniques based on tracer particle imaging are widely employed in flow diagnostics. However， their application in complex flow environments is inevitably challenged by aero-optical aberrations. For instance， in combustion or supersonic/hypersonic environments， refractive index fields with drastic spatial variations induce severe aero optical effects， causing significant degradation of tracer particle images and compromising the accuracy of velocity measurements. To mitigate this issue， a novel technical approach for the non-blind restoration of degraded images of tracer particles via Singular Value Decomposition （SVD） of the Point Spread Function （PSF） is proposed. This method first performs SVD on PSFs obtained at multiple calibration positions within the field of view and subsequently reconstructs the full-field PSF distribution efficiently using a limited number of spatial modes and their corresponding spatial weighting coefficients. Furthermore， a Total Variation （TV） regularized Richardson-Lucy iterative deconvolution algorithm is employed to perform non-blind restoration on the degraded particle images using the reconstructed local PSFs. Through various numerical simulations， the influence of the number of SVD modes and image noise levels on the restoration performance is systematically investigated， and the restoration performance is compared with classical restoration algorithms. The results show that the proposed method works effectively in processing the sparse particle fields. It effectively recovers particle morphology blurred by aero-optical effects and substantially enhances the Peak Signal-to-Noise Ratio （PSNR） and Structural Similarity Index Measure （SSIM） of the images， offering a new perspective for the application of tracer-based velocimetry in harsh optical environments.
| [1] | 李拓， 张清福， 潘翀， 等. 基于粒子图像分割的混合PIV-PTV算法［J］. 空气动力学学报， 2024， 42（2）： 68-75. |
| LI T， ZHANG Q F， PAN C， et al. Hybrid PIV-PTV algorithm based on particle image segmentation［J］. Acta Aerodynamica Sinica， 2024， 42（2）： 68-75 （in Chinese）. | |
| [2] | 邓志文， 何创新， 刘应征. 耦合粒子图像测速误差的连续伴随数据同化技术［J］. 航空学报， 2022， 43（5）： 125305. |
| DENG Z W， HE C X， LIU Y Z. Continuous-adjoint based data assimilation technique coupled with particle image velocimetry error［J］. Acta Aeronautica et Astronautica Sinica， 2022， 43（5）： 125305 （in Chinese）. | |
| [3] | SCHR?DER A， SCHANZ D. 3D Lagrangian particle tracking in fluid mechanics［J］. Annual Review of Fluid Mechanics， 2023， 55： 511-540. |
| [4] | ELREFAIE M， HüTTIG S， GLADKOVA M， et al. On-site aerodynamics using stereoscopic PIV and deep optical flow learning［J］. Experiments in Fluids， 2024， 65（12）： 183. |
| [5] | JIN Y， ZHANG W Q， SONG Y， et al. Three-dimensional rapid flame chemiluminescence tomography via deep learning［J］. Optics Express， 2019， 27（19）： 27308-27334. |
| [6] | WIENEKE B. Improvements for volume self-calibration［J］. Measurement Science and Technology， 2018， 29（8）： 084002. |
| [7] | HEMAYED E E. A survey of camera self-calibration［C］∥ Proceedings of the IEEE Conference on Advanced Video and Signal Based Surveillance， 2003. Piscataway： IEEE Press， 2003： 351-357. |
| [8] | 窦建宇， 潘翀. 基于神经网络的体视PIV空间标定模型［J］. 航空学报， 2021， 42（4）： 524720. |
| DOU J Y， PAN C. Spatial calibration model of stereo PIV based on neural network［J］. Acta Aeronautica et Astronautica Sinica， 2021， 42（4）： 524720 （in Chinese）. | |
| [9] | MARXEN M， SULLIVAN P E， LOEWEN M R， et al. Comparison of Gaussian particle center estimators and the achievable measurement density for particle tracking velocimetry［J］. Experiments in Fluids， 2000， 29（2）： 145-153. |
| [10] | K?HLER C J， SCHARNOWSKI S， CIERPKA C. On the uncertainty of digital PIV and PTV near walls［J］. Experiments in Fluids， 2012， 52（6）： 1641-1656. |
| [11] | 丁文锋， 万年， 赵彪， 等. 航空航天先进制造理论与技术研究现状及趋势［J］. 航空学报， 2025， 46（6）： 531309. |
| DING W F， WAN N， ZHAO B， et al. Research status and tendency of advanced manufacturing theory and technology in aerospace［J］. Acta Aeronautica et Astronautica Sinica， 2025， 46（6）： 531309 （in Chinese）. | |
| [12] | MANDARINO J A. The Gladstone-Dale relationship- Part Ⅲ， some general applications［J］. The Canadian Mineralogist， 1979， 17（1）： 71-76. |
| [13] | VANSELOW C， ST?BENER D， KIEFER J， et al. Particle image velocimetry in refractive index fields of combustion flows［J］. Experiments in Fluids， 2019， 60（10）： 149. |
| [14] | ELSINGA G E， VAN OUDHEUSDEN B W， SCARANO F. Evaluation of aero-optical distortion effects in PIV［J］. Experiments in Fluids， 2005， 39（2）： 246-256. |
| [15] | ZHENG Y T， HE Y Z， CHEN J R， et al. Instantaneous refractive index compensation on the velocity measurement using simultaneous PIV-BOST［J］. Experiments in Fluids， 2025， 66（9）： 164. |
| [16] | STELLA A， GUJ G， KOMPENHANS J， et al. Application of particle image velocimetry to combusting flows： design considerations and uncertainty assessment［J］. Experiments in Fluids， 2001， 30（2）： 167-180. |
| [17] | GOMIT G， CHATELLIER L， CALLUAUD D， et al. Free surface measurement by stereo-refraction［J］. Experiments in Fluids， 2013， 54（6）： 1540. |
| [18] | RAFFEL M， KOST F. Investigation of aerodynamic effects of coolant ejection at the trailing edge of a turbine blade model by PIV and pressure measurements［J］. Experiments in Fluids， 1998， 24（5）： 447-461. |
| [19] | KAISER S A， FRANK J H， LONG M B. Use of Rayleigh imaging and ray tracing to correct for beam-steering effects in turbulent flames［J］. Applied Optics， 2005， 44（31）： 6557. |
| [20] | HAERTIG J， HAVERMANN M， REY C， et al. Particle image velocimetry in Mach 3.5 and 4.5 shock-tunnel flows［J］. AIAA Journal， 2002， 40（6）： 1056-1060. |
| [21] | ELSINGA G E， ORLICZ G C. Particle imaging through planar shock waves and associated velocimetry errors［J］. Experiments in Fluids， 2015， 56（6）： 129. |
| [22] | LI H X， FISCHER A， AVILA M， et al. Measurement error of tracer-based velocimetry in single-phase turbulent flows with inhomogeneous refractive indices［J］. Experimental Thermal and Fluid Science， 2022， 136： 110681. |
| [23] | GAO Z Y， RADNER H， BüTTNER L， et al. Distortion correction for particle image velocimetry using multiple-input deep convolutional neural network and Hartmann-Shack sensing［J］. Optics Express， 2021， 29（12）： 18669. |
| [24] | RICHARDSON W H. Bayesian-based iterative method of image restoration［J］. Journal of the Optical Society of America， 1972， 62（1）： 55. |
| [25] | TURCOTTE R， SUTU E， SCHMIDT C C， et al. Deconvolution for multimode fiber imaging： Modeling of spatially variant PSF［J］. Biomedical Optics Express， 2020， 11（8）： 4759-4771. |
| [26] | WHITE R L. Image restoration using the damped Richardson-Lucy method［C］∥ Instrumentation in Astronomy Ⅷ. Bellingham： SPIE， 1994： 1342-1348. |
| [27] | TAI Y W， TAN P， BROWN M S. Richardson-Lucy deblurring for scenes under a projective motion path［J］. IEEE Transactions on Pattern Analysis and Machine Intelligence， 2011， 33（8）： 1603-1618. |
| [28] | DEY N， BLANC-FERAUD L， ZIMMER C， et al. Richardson-Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution［J］. Microscopy Research and Technique， 2006， 69（4）： 260-266. |
| [29] | INGARAMO M， YORK A G， HOOGENDOORN E， et al. Richardson-Lucy deconvolution as a general tool for combining images with complementary strengths［J］. ChemPhysChem， 2014， 15（4）： 794-800. |
| [30] | GRAVEL P， SURTI S， KRISHNAMOORTHY S， et al. Spatially-variant image-based modeling of PSF deformations with application to a limited angle geometry from a dual-panel breast-PET imager［J］. Physics in Medicine & Biology， 2019， 64（22）： 225015. |
| [31] | TRUSSELL H， HUNT B. Sectioned methods for image restoration［J］. IEEE Transactions on Acoustics， Speech， and Signal Processing， 1978， 26（2）： 157-164. |
| [32] | LAUER T. Deconvolution with a spatially-variant PSF［C］∥ Astronomical Data Analysis Ⅱ. Bellingham： SPIE， 2002， 4847： 167. |
| [33] | NAGY J G， O’LEARY D P. Restoring images degraded by spatially variant blur［J］. SIAM Journal on Scientific Computing， 1998， 19（4）： 1063-1082. |
| [34] | O’CONNOR D， VANDENBERGHE L. Total variation image deblurring with space-varying kernel［J］. Computational Optimization and Applications， 2017， 67（3）： 521-541. |
| [35] | SCHULER C J， BURGER H C， HARMELING S， et al. A machine learning approach for non-blind image deconvolution［C］∥ 2013 IEEE Conference on Computer Vision and Pattern Recognition. Piscataway： IEEE Press， 2013： 1067-1074. |
| [36] | 熊渊. 背景纹影测量技术研究与应用进展［J］. 实验流体力学， 2022， 36（2）： 30-48. |
| XIONG Y. Recent advances in background oriented Schlieren and its applications［J］. Journal of Experiments in Fluid Mechanics， 2022， 36（2）： 30-48 （in Chinese）. | |
| [37] | RAJENDRAN L K， BANE S P M， VLACHOS P P. PIV/BOS synthetic image generation in variable density environments for error analysis and experiment design［J］. Measurement Science and Technology， 2019， 30（8）： 085302. |
| [38] | J?HNE B. Digital image processing［M］. Berlin： Springer， 2005. |
| [39] | BECK A， TEBOULLE M. Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems［J］. IEEE Transactions on Image Processing， 2009， 18（11）： 2419-2434. |
| [40] | HORé A， ZIOU D. Image quality metrics： PSNR vs. SSIM［C］∥ 2010 20th International Conference on Pattern Recognition. Piscataway： IEEE Press， 2010： 2366-2369. |
| [41] | WANG Z， BOVIK A C， SHEIKH H R， et al. Image quality assessment： from error visibility to structural similarity［J］. IEEE Transactions on Image Processing， 2004， 13（4）： 600-612. |
| [42] | LI J， XIONG Y， TANG Y， et al. Three-dimensional diagnosis of lean premixed turbulent swirl flames using tomographic background oriented Schlieren［J］. Physics of Fluids， 2024， 36（5）： 1-10. |
| [43] | LI J W， MENG X H， XIONG Y， et al. Neural deflection field for sparse-view tomographic background oriented Schlieren［J］. Physics of Fluids， 2024， 36（12）： 121701. |
| [44] | PAN G Z， SHEN J Q， LI X， et al. Comprehensive error analysis framework for Shack-Hartmann wavefront measurements in aero-optical applications［J］. Physics of Fluids， 2025， 37（8）： 081707. |
| [45] | HANSEN P C. Analysis of discrete ill-posed problems by means of the L-curve［J］. SIAM Review， 1992， 34（4）： 561-580. |
/
| 〈 |
|
〉 |
CJA