Comparison Between Regularized Optimization Algorithms for Tomographic Reconstruction of Plume Cross Sections in the Atmosphere

We analyze and compare two approaches for the tomographic reconstruction of trace gas distributions in the atmosphere, adapted to differential optical absorption spectroscopy (DOAS) applications. The first approach performs the inversion by solving a regularized least squares problem. Regularization is required because the retrieval of the distribution from a limited set of measurements is an ill-posed problem. This approach does not consider the nonnegativity of the trace gas concentrations. The second approach is a new proposal that solves an optimization problem with the Laplacian of the solution as the regularization term. This approach enables the possibility of adding the nonnegativity constraint to the solution. The algorithm here is stated as an instance of a convex optimization problem and can numerically be solved using, for example, the CVX package. We test both approaches on reconstructions of simulated gas distributions and different experimental configurations applicable to Multi-Axis DOAS and multispectral imaging measurements. From the results, we can then determine a set of reconstruction parameters appropriate to real plume measurements.