SOURCE RECONSTRUCTION WITH MULTIFREQUENCY SPARSE SCATTERED FIELDS

We consider the reconstruction of acoustic sources with multifrequency sparse scattered fields. Specifically, we shall use the multifrequency scattered fields at finitely many measurement points to prove some uniqueness results and introduce three numerical schemes. The underlying sources can be an extended source or a sum of monopoles and dipoles. At a fixed measurement point, we show that the spheres centered at the point passing through the point sources can be uniquely determined by the multifrequency scattered fields. For M multipolar point sources, the uniqueness for locating the positions and recovering scattering strengths has been proved using multifrequency scattered fields for at most 6M + 1 measurement points. For an extended source, we show that the smallest annular containing the source centered at the measurement point can be uniquely determined by the multifrequency scattered field. Motivated by the uniqueness proofs, we then introduce three schemes for reconstructing the sources. Some numerical examples in three dimensions are presented to show the validity and robustness of the proposed numerical schemes.