  The problem of recovering acoustic sources, more specifically monopoles, from
point-wise measurements of the corresponding acoustic pressure at a limited
number of frequencies is addressed. To this purpose, a family of sparse
optimization problems in measure space in combination with the Helmholtz
equation on a bounded domain is considered. A weighted norm with unbounded
weight near the observation points is incorporated into the formulation.
Optimality conditions and conditions for recovery in the small noise case are
discussed, which motivates concrete choices of the weight. The numerical
realization is based on an accelerated conditional gradient method in measure
space and a finite element discretization.
