  We study the shape reconstruction of a dielectric inclusion from the faraway
measurement of the associated electric field. This is an inverse problem of
practical importance in biomedical imaging and is known to be notoriously
ill-posed. By incorporating Drude's model of the dielectric parameter, we
propose a novel reconstruction scheme by using the plasmon resonance with a
significantly enhanced resonant field. We conduct a delicate sensitivity
analysis to establish a sharp relationship between the sensitivity of the
reconstruction and the plasmon resonance. It is shown that when plasmon
resonance occurs, the sensitivity functional blows up and hence ensures a more
robust and effective construction. Then we combine the Tikhonov regularization
with the Laplace approximation to solve the inverse problem, which is an
organic hybridization of the deterministic and stochastic methods and can
quickly calculate the minimizer while capture the uncertainty of the solution.
We conduct extensive numerical experiments to illustrate the promising features
of the proposed reconstruction scheme.
