Fitting local, low-dimensional parameterizations of optical turbulence modeled from optimal transport velocity vectors

Abstract

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.