Fioralba Cakoni, David Colton
abstract:
The linear sampling method is an algorithm for solving the inverse scattering
problem for acoustic and electromagnetic waves. The method is based on showing
that a linear integral equation of first kind has a solution that becomes
unbounded as a parameter z approaches the boundary of the scatterer D
from inside D. However, except for the case of the transmission problem,
the case where z is in the exterior of D is unresolved. Since for the
inverse scattering problem D is unknown, this step is crucial for the
mathematical justification of the linear sampling method. In this paper we give
a mathematical justification of the linear sampling method for arbitrary z
by using the theory of integral equations of first kind with singular kernels.