Stability for the Acoustic Inverse Source Problem in Inhomogeneous Media

Source abstract

In this paper, we show for the first time the stability of the inverse source problem for the three-dimensional Helmholtz equation in an inhomogeneous background medium. The stability estimate consists of the Lipschitz type data discrepancy and the high frequency tail of the source function, where the latter decreases as the upper bound of the frequency increases. The analysis employs scattering theory to obtain the holomorphic domain and an upper bound for the resolvent of the elliptic operator.