  We develop a novel wave imaging scheme for reconstructing the shape of an
inhomogeneous scatterer and we consider the inverse acoustic obstacle
scattering problem as a prototype model for our study. There exists a wealth of
reconstruction methods for the inverse obstacle scattering problem and many of
them intentionally avoid the interior resonant modes. Indeed, the occurrence of
the interior resonance may cause the failure of the corresponding
reconstruction. However, based on the observation that the interior resonant
modes actually carry the geometrical information of the underlying obstacle, we
propose an inverse scattering scheme of using those resonant modes for the
reconstruction. To that end, we first develop a numerical procedure in
determining the interior eigenvalues associated with an unknown obstacle from
its far-field data based on the validity of the factorization method. Then we
propose two efficient optimization methods in further determining the
corresponding eigenfunctions. Using the afore-determined interior resonant
modes, we show that the shape of the underlying obstacle can be effectively
recovered. Moreover, the reconstruction yields enhanced imaging resolution,
especially for the concave part of the obstacle. We provide rigorous
theoretical justifications for the proposed method. Numerical examples in 2D
and 3D verify the theoretically predicted effectiveness and efficiency of the
method.
