Physics-driven single-frame turbulence restoration via Beltrami-supervised quasi-conformal mapping

Atmospheric turbulence degrades long-range imaging through entangled spatially varying blur, geometric tilt, and sensor noise. Current single-frame methods predominantly focus on deblurring, often failing to recover dense tilt fields and introducing non-physical artifacts. We propose TurbWNet, a physics-driven cascade framework that rigorously inverts this degradation process. A novel quasi-conformal tilt estimation module, to our knowledge, supervised by Beltrami coefficients, mathematically guarantees the deformation field's topological integrity, eliminating catastrophic mesh folding. Evaluated on public benchmarks, TurbWNet outperforms recent leading algorithms in single-frame restoration by up to 1.50 dB in PSNR. The code is publicly available.