A. Greenleaf et G. Uhlmann, RECOVERING SINGULARITIES OF A POTENTIAL FROM SINGULARITIES OF SCATTERING DATA, Communications in Mathematical Physics, 157(3), 1993, pp. 549-572
In this paper we show that the leading singularities of certain potent
ials can be determined from the leading singularities of the backscatt
ering (as well as other determined sets of scattering data). The poten
tials in question are conormal with respect to smooth surfaces of arbi
trary dimension; the restrictions on their orders allow for unbounded
potentials in all dimension greater than or equal to three.