10 years of matching pursuits for inverse problems: what’s been done and what’s to come

In the light of significant challenges like the climate change, the visualization of the gravitational potential remains a priority in geodesy. A decade ago, the Geomathematics Group Siegen proposed alternative representations for such problems.

The respective methods are based on matching pursuits: hence, they build a representation in a so-called best basis. However, they include additional aspects which occur, for instance, when the downward continuation of the gravitational potential is approximated.

In this talk, we summarize the different developmental stages from 2011 up to now which started with a basic implementation and then included aspects of orthogonality, weakness and dictionary learning, respectively. Further, we give an outlook on our next steps with these methods. For the current status-quo, we show numerical results with respect to the downward continuation of the gravitational potential.