Identification of point like objects with multi-frequency sparse data

The inverse acoustic scattering of point objects using multi-frequency sparse measurements are studied. The objects may be a sum of point sources or point like scatterers. We show that the locations and scattering strengths of the point objects can be uniquely identified by the multi-frequency near or far fields taken at sparse sensors. Based on the uniqueness analysis, some direct methods have also been proposed for reconstructing the locations and determining the scattering strengths. The numerical examples are conducted to show the validity and robustness of the proposed numerical methods.