Random walk models for geometry-driven image super-resolution

This paper addresses stochastic geometry-driven image models and its application to super-resolution issues. Whereas most stochastic image models rely on some priors on the distribution of grey-level configurations (e.g., patch-based models, Markov priors, multiplicative cascades,...), we here focus on geometric priors. We aim at simulating texture samples while controlling high-resolution geometrical features. In this respect, we introduce a stochastic model for texture orientation fields stated as a 2D Orstein-Uhlenbeck process. We show that this process resorts in the stationary case to priors on orientation statistics. We exploit this model to state image super-resolution as a geometry-driven variational minimization, where the geometry is sampled from the proposed conditional 2D Orstein-Uhlenbeck process. We demonstrate the relevance of this approach for real images associated with the remote sensing of ocean surface dynamics.