Study on Parameter Choice Methods for the RFMP with Respect to Downward Continuation - Gutting, Martin; Kretz, Bianca; Michel, Volker; Telschow, Roger (Frontiers in Applied Mathematics and Statistics, 2017)
Recently, the regularized functional matching pursuit (RFMP) was introduced as a greedy algorithm for linear ill-posed inverse problems. This algorithm incorporates the Tikhonov-Phillips regularization which implies the necessity of a parameter choice. In this paper, some known parameter choice methods are evaluated with respect to their performance in the RFMP and its enhancement, the regularized orthogonal functional matching pursuit (ROFMP). As an example of a linear inverse problem, the downward continuation of gravitational field data from the satellite orbit to the Earth's surface is chosen, because it is exponentially ill-posed. For the test scenarios, different satellite heights with several noise-to-signal ratios and kinds of noise are combined. The performances of the parameter choice strategies in these scenarios are analyzed. For example, it is shown that a strongly scattered set of data points is an essentially harder challenge for the regularization than a regular grid. The obtained results yield, as a first orientation, that the generalized cross validation, the L-curve method and the residual method could be most appropriate for the RFMP and the ROFMP.