Sparse optimization for inverse problems in atmospheric modelling

We consider inverse problems in atmospheric modelling represented by a linear system which is based on a source-receptor sensitivity matrix and measurements. Instead of using the ordinary least squares, we add a weighting matrix based on the topology of measurement points and show the connection with Bayesian modelling. Since the source-receptor sensitivity matrix is usually ill-conditioned, the problem is often regularized, either by perturbing the objective function or by modifying the sensitivity matrix. However, both these approaches may be heavily dependent on specified parameters. To ease this burden, we propose to use techniques looking for a sparse solution with a small number of positive elements. Finally, we compare all these methods on the European Tracer Experiment (ETEX) data where there is no apriori information apart from the release position and some measurements.