ACTA AERONAUTICAET ASTRONAUTICA SINICA >
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
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.
Huan WU , Weiran WANG , Yuan XIONG , Chong PAN , Jinjun WANG . A novel approach for non-blind restoration of optically degraded images of tracer particles[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2026 , 47(16) : 133145 -133145 . DOI: 10.7527/S1000-6893.2026.33145
| [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. |
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