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In this paper, we are concerned with the recovery of the geometric shapes ofinhomogeneous inclusions from the associated far field data in electrostaticsand acoustic scattering. We present a local resolution analysis and show thatthe local shape around a boundary point with a high magnitude of mean curvaturecan be reconstructed more easily and stably. In proving this, we develop anovel mathematical scheme by analyzing the generalized polarisation tensors(GPTs) and the scattering coefficients (SCs) coming from the associatedscattered fields, which in turn boils down to the analysis of the layerpotential operators that sit inside the GPTs and SCs via the microlocalanalysis. In a delicate and subtle manner, we decompose the reconstructionprocess into several steps, where all but one steps depend on the globalgeometry, and one particular step depends on the mean curvature at a givenboundary point. Then by a sensitivity analysis with respect to localperturbations of the curvature of the boundary surface, we establish the localresolution effects. Our study opens up a new field of mathematical analysis onwave super-resolution imaging.

Localized sensitivity analysis at high-curvature boundary points of reconstructing inclusions in transmission problems