  Point source localisation is generally modelled as a Lasso-type problem on
measures. However, optimisation methods in non-Hilbert spaces, such as the
space of Radon measures, are much less developed than in Hilbert spaces. Most
numerical algorithms for point source localisation are based on the Frank-Wolfe
conditional gradient method, for which ad hoc convergence theory is developed.
We develop extensions of proximal-type methods to spaces of measures. This
includes forward-backward splitting, its inertial version, and primal-dual
proximal splitting. Their convergence proofs follow standard patterns. We
demonstrate their numerical efficacy.
