LASSO - An iterative framework for probe methods

We present a new iterative version of the singular sources method (or probe method) for the reconstruction of scatterers from the far field pattern of scattered acoustic or electromagnetic waves. The scheme is based on the construction of an indicator function given by the scattered field for incident point sources in its source point from the given far field patterns for plane waves. The indicator function is then used to drive the contraction of a surface which surrounds the unknown scatterers. A stopping criterion for those parts of the surfaces which touch the unknown scatterers is formulated. A splitting approach for the contracting surfaces is formulated, such that scatterers consisting of several separate components can be reconstructed. Convergence of the scheme is shown and we demonstrate its feasibility by a numerical study with several examples.