L. Paivarinta et V. Serov, RECOVERY OF SINGULARITIES OF A MULTIDIMENSIONAL SCATTERING POTENTIAL, SIAM journal on mathematical analysis, 29(3), 1998, pp. 697-711
We prove that in multidimensional potential scattering the leading ord
er singularities of the unknown potential are obtained exactly from th
e scattering amplitude by the linearized inversion method. The proof i
s based on the appropriate mapping properties of the fundamental solut
ion in weighted L-p-spaces and on a homogeneity argument concerning th
e bilinear term.