  Consider the scattering of a time-harmonic plane wave by heterogeneous media
consisting of linear or nonlinear point scatterers and extended obstacles. A
generalized Foldy-Lax formulation is developed to take fully into account of
the multiple scattering by the complex media. A new imaging function is
proposed and an FFT-based direct imaging method is developed for the inverse
obstacle scattering problem, which is to reconstruct the shape of the extended
obstacles. The novel idea is to utilize the nonlinear point scatterers to
excite high harmonic generation so that enhanced imaging resolution can be
achieved. Numerical experiments are presented to demonstrate the effectiveness
of the proposed method.
