  This paper investigates the shape reconstructions of sub-wavelength objects
from near-field measurements in transverse electromagnetic scattering. This
geometric inverse problem is notoriously ill-posed and challenging. We develop
a novel reconstruction scheme using plasmon resonances with significantly
enhanced sensitivity and resolution. First, by spectral analysis, we establish
a sharp quantitative relationship between the sensitivity of the reconstruction
and the plasmon resonance. It shows that the sensitivity functional blows up
when plasmon resonance occurs. Hence, the signal-to-noise ratio is
significantly improved and the robustness and effectiveness of the
reconstruction are ensured. Second, a variational regularization method is
proposed to overcome the ill-posedness, and an alternating iteration method is
introduced to automatically select the regularization parameters. Third, we use
the Laplace approximation method to capture the statistical information of the
target scattering object. Both rigorous theoretical analysis and extensive
numerical experiments are conducted to validate the promising features of our
method.
