Physical-model based reconstruction of the global instantaneous velocity field from velocity measurement at a few points

The problem of reconstruction of a global velocity field is an ill-posed inverse problem, which needs to be regularized so as to be solved. In this paper, we present a new model of regularization for this problem. This model is based on physical properties of fluid mechanics and is performed within the framework of global Bayesian decision theory and the framework of Markov random fields models. Once the problem is defined in terms of this anisotropic Markovian model, it is transformed into the optimization of an energy and is solved thanks to a multiscale relaxation scheme. Since in case of non-uniformly distributed observations, the classical multiscale relaxation is limited, we propose a new method of relaxation, involving the computation of an adaptive non-uniform grid fitted to the spatial repartition of the data, thanks to a self-organizing neural network