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

## TL;DR

This paper introduces a fast, FFT-based direct imaging method for inverse obstacle scattering that leverages nonlinear point scatterers to generate high harmonics, improving imaging resolution of extended obstacles.

## Contribution

A novel imaging approach that incorporates nonlinear point scatterers and high harmonic generation within a generalized Foldy-Lax framework for better obstacle reconstruction.

## Key findings

- Effective imaging of extended obstacles demonstrated through numerical experiments.
- Enhanced resolution achieved using nonlinear point scatterers and high harmonic generation.

## Abstract

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.