Patch-based regression for reference-robust atmospheric turbulence correction in outdoor optical systems

Atmospheric turbulence severely degrades long-range optical systems through geometric distortions and temporal blur, limiting performance in free-space optical communication, surveillance, and remote sensing applications. This work focuses on the geometric component of turbulence-induced distortion (random warping and temporal jitter) and does not target blur removal or restoration of a latent sharp image. A critical but often overlooked challenge in geometric turbulence correction is sensitivity to reference frame construction, which is rarely optimal in operational deployments. We present a lightweight patch-based regression approach that learns a direct mapping from local image patches to displacement vectors through ridge regression, replacing full-resolution optical flow at the fine registration stage. The approach requires no GPU resources, minimal training data, and has a closed-form solution, which makes it a practical study instrument for systematic sensitivity analysis across diverse reference constructions and atmospheric conditions. The method is evaluated on real long-range time-lapse imagery acquired over a 20 km near-ground horizontal propagation path (Jornada Experimental Range, New Mexico) and short-range video data over 200 and 100 m optical paths (Bars/Stripes dataset). Using mean squared error (MSE) and structural similarity index measure (SSIM), patch-based regression consistently outperforms Farnebäck optical flow across all tested sequences: 63% versus 44% MSE improvement (July 17), 26% versus 8.5% (July 20), 75.5% versus 60.3% (Bars/Stripes Sequence 1), and 79.9% versus 72.8% (Bars/Stripes Sequence 2), with consistently higher SSIM in all cases. Robustness to reference construction is quantified by varying the number of frames N used to build the reference and computing the coefficient of variation (CV) of improvement across N . For long-range data, optical flow exhibits high variability (CV=17.7% and 87.4%), whereas patch-based regression remains substantially more stable (CV=7.7% and 17.9%). For short-range data, patch-based regression consistently reduces CV from 9.1% to 4.5% (Sequence 1) and from 5.7% to 3.6% (Sequence 2). Under an alternative lucky-frame reference strategy, patch regression maintains its advantage across all datasets with gains of 10.5–27.4 percentage points, confirming that the performance advantage generalizes across different reference construction strategies. These results demonstrate that patch-based regression provides a practical, reference-robust baseline for studying turbulence correction sensitivity in outdoor optical systems operating under real atmospheric propagation conditions.