Super-resolution in Imaging High Contrast Targets from the Perspective of Scattering Coefficients

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.