Study on parameter choice methods for the RFMP with respect to downward continuation

TL;DR

This paper evaluates various parameter choice methods for the RFMP and ROFMP algorithms in solving the exponentially ill-posed problem of downward continuation of gravitational data, considering different noise and data configurations.

Contribution

It provides a comparative analysis of parameter choice strategies for RFMP and ROFMP in a challenging inverse problem setting, guiding their practical application.

Findings

Certain parameter choice methods perform better with regular grid data.

Scattered data points pose greater challenges for regularization.

The study offers initial guidance on feasible parameter strategies for RFMP and ROFMP.

Abstract

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.