A review and examination of results on uniqueness in inverse problems
Article first published online: 7 DEC 2012
Copyright 1987 by the American Geophysical Union.
Volume 22, Issue 6, pages 1026–1030, November 1987
How to Cite
1987), A review and examination of results on uniqueness in inverse problems, Radio Sci., 22(6), 1026–1030, doi:10.1029/RS022i006p01026.(
- Issue published online: 7 DEC 2012
- Article first published online: 7 DEC 2012
- Manuscript Accepted: 2 MAR 1987
- Manuscript Received: 3 DEC 1986
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.