GPS tomography of the ionospheric electron content with a correlation functional

We develop a minimization functional in order to regularize the inverse problem associated with three-dimensional ionospheric stochastic tomography. This functional is designed to yield, upon minimization, a solution which maximizes the frequency content of the solution below a certain cutoo, while keeping 2 constant. We show how this functional can be rewritten in terms of the correlation function of the image, thereby facilitating the algorithmic implementation of the method. We then implement this functional in a Kalman lter and obtain a smoothing algorithm that acts in both space and time. Finally, we use this technique to perform global scale GPS tomography of the ionospheric electron content.