Source identification from line integral measurements and simple atmospheric models

We consider the problem of estimating the sparse initial condition of a solution to the advection-difiusion equation based on line integrals of the solution at a later time. We propose models for locating a single and multiple point sources. We also propose algorithms for the effcient implementation of these models. In practice, the models are relevant also for reconstructing the solution of the PDE at the observation time from a very sparse Radon transform; in this case, our models improve on more standard Radon inversion techniques by utilizing the specialized information about how the observed function was generated.