  In this paper we consider the inverse scattering problem for high-contrast
targets. We mathematically analyze the experimentally-observed phenomenon of
super-resolution in imaging the target shape. This is the first time that a
mathematical theory of super-resolution has been established in the context of
imaging high contrast inclusions. We illustrate our main findings with a
variety of numerical examples. Our analysis is based on the novel concept of
scattering coefficients. These findings may help in developing resonant
structures for resolution enhancement.
