  We present in this paper a novel numerical reconstruction method for solving
a 3D coefficient inverse problem with scattering data generated by a single
direction of the incident plane wave. This inverse problem is well-known to be
a highly nonlinear and ill-posed problem. Therefore, optimization-based
reconstruction methods for solving this problem would typically suffer from the
local-minima trapping and require strong a priori information of the solution.
To avoid these problems, in our numerical method, we aim to construct a cost
functional with a globally strictly convex property, whose minimizer can
provide a good approximation for the exact solution of the inverse problem. The
key ingredients for the construction of such functional are an
integro-differential formulation of the inverse problem and a Carleman weight
function. Under a (partial) finite difference approximation, the global strict
convexity is proven using the tool of Carleman estimates. The global
convergence of the gradient projection method to the exact solution is proven
as well. We demonstrate the efficiency of our reconstruction method via a
numerical study of experimental backscatter data for buried objects.
