  This paper is concerned with the inverse problem of reconstructing a small
object from far field measurements. The inverse problem is severally ill-posed
because of the diffraction limit and low signal to noise ratio. We propose a
novel methodology to solve this type of inverse problems based on an idea from
plasmonic sensing. By using the field interaction with a known plasmonic
particle, the fine detail information of the small object can be encoded into
the shift of the resonant frequencies of the two particle system in the far
field. In the intermediate interaction regime, we show that this information is
exactly the generalized polarization tensors associated with the small object,
from which one can perform the reconstruction. Our theoretical findings are
supplemented by a variety of numerical results. The results in the paper also
provide a mathematical foundation for plasmonic sensing.
