Ionospheric tomography in Bayesian framework with Gaussian Markov random field priors

We present a novel ionospheric tomography reconstruction method. The method is based on Bayesian inference with the use of Gaussian Markov random field priors. We construct the priors as a system of stochastic partial differential equations. Numerical approximations of these equations can be represented with linear systems with sparse matrices, therefore providing computational efficiency. The method enables an interpretable scheme to build the prior distribution based on physical and empirical information on the structure of the ionosphere. We show through synthetic test cases in a two-dimensional setup of latitude-altitude slices how this method can be applied to satellite-based ionospheric tomography and how information about the structure of the ionosphere can be implemented in the prior. The technique is capable of being easily extended to multifrequency tomographic analysis or used for the inclusion of other data sets of ionospheric electron density, such as ground-based observations by radars or ionosondes.