On the multi-frequency inverse source problem in heterogeneous media

Abstract

The inverse source problem where an unknown source is to be identified from knowledge of its radiated wave is studied. The focus is placed on the effect that multi-frequency data have on establishing uniqueness. In particular, it is shown that data obtained from finitely many frequencies are not sufficient. On the other hand, if the frequency varies within a set with an accumulation point, then the source is determined uniquely, even in the presence of highly heterogeneous media. In addition, an algorithm for the reconstruction of the source using multi-frequency data is proposed. The algorithm, based on a subspace projection method, approximates the minimum-norm solution given the available multi-frequency measurements. A few numerical examples are presented.