Power laws and inverse motion modeling: application to turbulence measurements from satellite images

In the context of tackling the ill-posed inverse problem of motion estimation from image sequences, we propose to introduce prior knowledge on flow regularity given by turbulence statistical models. Prior regularity is formalized using turbulence power laws describing statistically self-similar structure of motion increments across scales. The motion estimation method minimizes the error of an image observation model while constraining second order structure function to behave as a power law within a prescribed range. Thanks to a Bayesian modeling framework, the motion estimation method is able to jointly infer the most likely power law directly from image data. The method is assessed on velocity fields of 2D or quasi-2D flows. Estimation accuracy is first evaluated on a synthetic image sequence of homogeneous and isotropic 2D turbulence. Results obtained with the approach based on physics of fluids outperforms state-of-the-art. Then, the method analyzes atmospheric turbulence using a real meteorological image sequence. Selecting the most likely power law model enables the recovery of physical quantities which are of major interest for turbulence atmospheric characterization. In particular, from meteorological images we are able to estimate energy and enstrophy fluxes of turbulent cascades, which are in agreement with previous in situ measurements.