This work exploits a connection between optimal transport theory and the physics of image propagation to yield a locally low-dimensional model of turbulence-corrupted imagery. Optimal transport produces an invertible, pixel-wise linear trajectories to approximate the globally nonlinear turbulence between a clean and turbulence corrupted image pair. We use the low-dimensional model to fit subsets of the optimal transport vector fields and stitch the local models into a surrogate for the global map to be used for image cleaning. Experiments are performed on laboratory generated data of beam propagation using different values of the Fried parameter (a scale measuring turbulence coherence) as well as a toy data set. The results suggest this is a fruitful direction, and first step, towards using multiple realizations of turbulence corrupted images to learn a blind surrogate for the optimal transport vector field for image cleaning.

这项工作利用了最佳输运理论和图像传播物理学之间的联系，以产生局部低维的湍流图像模型。最佳传输会产生一个可逆的像素级线性轨迹，以近似于干净和湍流破坏的图像对之间的全局非线性湍流。我们使用低维模型来拟合最佳运输矢量场的子集，并将局部模型缝合到用于图像清洁的全局地图的替代中。使用Fried参数（测量湍流相干性的标度）的不同值以及玩具数据集对实验室生成的光束传播数据进行实验。结果表明这是一个富有成果的方向，而第一步，