Super-resolution in imaging high contrast targets from the perspective of scattering coefficients

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In this paper we consider the inverse scattering problem for high-contrast targets, and analyze mathematically the experimentally observed phenomenon about super-resolution in imaging the shapes of these targets. In particular, super-resolution at specific high contrast values is justified based on the novel concept of scattering coefficients and several important implications (given by two main theorems, Theorems 4.6 and 4.9). This is the first time that a mathematical theory of super-resolution is established in the context of imaging high-contrast inclusions. We shall also illustrate our main findings with a variety of numerical examples. These findings may help develop resonant structures for resolution enhancement.