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Consider the scattering of a time-harmonic plane wave by heterogeneous mediaconsisting of linear or nonlinear point scatterers and extended obstacles. Ageneralized Foldy-Lax formulation is developed to take fully into account ofthe multiple scattering by the complex media. A new imaging function isproposed and an FFT-based direct imaging method is developed for the inverseobstacle scattering problem, which is to reconstruct the shape of the extendedobstacles. The novel idea is to utilize the nonlinear point scatterers toexcite high harmonic generation so that enhanced imaging resolution can beachieved. Numerical experiments are presented to demonstrate the effectivenessof the proposed method.

A fast direct imaging method for the inverse obstacle scattering problem with nonlinear point scatterers