Reconstruction of multipolar point sources with multi-frequency sparse far field data

The inverse acoustic scattering of point sources using multi-frequency sparse far field patterns is studied. The object may be a sum of monopoles and dipoles. We show that the locations and scattering strengths of the point sources can be uniquely identified by the multi-frequency far fields taken at sparse observation directions. Based on the uniqueness analyses, two schemes are proposed to distinguish the dipoles and monopoles, locate the positions and recover the scattering strengths. Numerical examples in two dimensions are presented to validity the effectiveness and robustness of the proposed methods. In particular, the numerical reconstructions indicate that the proposed methods are fast, stable and independent of the types, number or positions of the unknown point sources.