Regularization parameter selection methods for an inverse dispersion problem

Abstract: There are many regularization parameter selection methods that can be used when solving inverse problems, but it is not clear which one is best suited for the inverse dispersion problem. The suitability of three different methods for solving the inverse dispersion problem are evaluated here in order to pick a suitable method for these kinds of problems in the future. The regularization parameter selection methods are used to solve the separable non-linear inverse dispersion problem which is adjusted and solved as a linear inverse problem. It is solved with Tikhonov regularization and the model is a time integrated Gaussian puff model. The dispersion problem is used with different settings and is solved with the three methods. The three methods are generalized cross-validation, L-curve method and quasi-optimality criterion. They produce rather different solutions and the results show that generalized cross-validation is the best choice. The other methods are less stable and the errors are sometimes orders of magnitude larger than the errors from generalized cross-validation.