  We propose a novel dictionary learning add-on for existing approximation
algorithms for spherical inverse problems such as the downward continuation of
the gravitational potential. The Inverse Problem Matching Pursuit (IPMP)
algorithms iteratively minimize the Tikhonov functional in order to construct a
weighted linear combination of so-called dictionary elements as a regularized
approximation. A dictionary is a set that contains trial functions such as
spherical harmonics (SHs), Slepian functions (SLs) as well as radial basis
functions (RBFs) and wavelets (RBWs). Previously, the IPMP algorithms worked
with finite dictionaries which are vulnerable regarding a possible biasing of
the outcome. Here, we propose an additional learning technique that allows us
to work with infinitely many trial functions and provides us with a learnt
dictionary for future use in the IPMP algorithms. We explain the general
mechanism and provide numerical results that prove its applicability and
efficiency.
