A novel approach for non-blind restoration of optically degraded images of tracer particles

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.