A review and examination of results on uniqueness in inverse problems

Abstract

Inverse source and inverse scattering problems represent distinct situations with regard to the uniqueness of their solutions, although they are often treated the same. This paper examines the reasons why the distinction between these two problems is critical in determining uniqueness. What is known about sufficient (and, in some cases, necessary) information to insure uniqueness for real‐world inverse problems is reviewed. Finally, although Hoenders' result is clear for the inverse scattering problem, there is some controversy over what set of constraints are necessary and sufficient to insure uniqueness in the inverse source problem. This is examined, and the origins of questions which arise from the usual derivations of the fields associated with nonradiating sources are explained.