Study on parameter choice methods for the RFMP with respect to downward continuation
This work provides a first orientation for selecting regularization parameters in greedy algorithms for ill-posed inverse problems, but the results are incremental and domain-specific.
The paper evaluates parameter choice methods for the regularized functional matching pursuit (RFMP) and its variant ROFMP in the context of downward continuation of gravitational field data, showing that scattered data points pose a greater challenge than regular grids.
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 a first orientation which parameter choice methods are feasible for the RFMP and the ROFMP.