  This paper concerns electromagnetic 3D subsurface imaging in connection with
sparsity of signal sources. We explored an imaging approach that can be
implemented in situations that allow obtaining a large amount of data over a
surface or a set of orbits but at the same time require sparsity of the signal
sources. Characteristic to such a tomography scenario is that it necessitates
the inversion technique to be genuinely three-dimensional: For example, slicing
is not possible due to the low number of sources. Here, we primarily focused on
astrophysical subsurface exploration purposes. As an example target of our
numerical experiments we used a synthetic small planetary object containing
three inclusions, e.g. voids, of the size of the wavelength. A tetrahedral
arrangement of source positions was used, it being the simplest symmetric point
configuration in 3D. Our results suggest that somewhat reliable inversion
results can be produced within the present a priori assumptions, if the data
can be recorded at a specific resolution. This is valuable early-stage
knowledge especially for design of future planetary missions in which the
payload needs to be minimized, and potentially also for the development of
other lightweight subsurface inspection systems.
