Constructing probing functions for direct sampling methods for inverse scattering problems with limited-aperture data: finite space framework and deep probing network

TL;DR

This paper develops a novel finite space framework and deep learning approach to enhance direct sampling methods for inverse scattering problems with limited-aperture data, overcoming resolution limits and improving estimation accuracy.

Contribution

It introduces a finite space framework combined with unsupervised deep learning to construct effective probing functions for limited-aperture inverse scattering problems.

Findings

Proposed schemes outperform traditional DSMs with limited data

Deep learning enhances resolution and stability of scatterer estimation

Numerical experiments validate the effectiveness of the new approach

Abstract

This work studies an inverse scattering problem when limited-aperture data are available that are from just one or a few incident fields. This inverse problem is highly ill-posed due to the limited receivers and a few incident fields employed. Solving inverse scattering problems with limited-aperture data is important in applications as collecting full data is often either unrealistic or too expensive. The direct sampling methods (DSMs) with full-aperture data can effectively and stably estimate the locations and geometric shapes of the unknown scatterers with a very limited number of incident waves. However, a direct application of DSMs to the case of limited receivers would face the resolution limit. To break this limitation, we propose a finite space framework with two specific schemes, and an unsupervised deep learning strategy to construct effective probing functions for the DSMs in the case with limited-aperture data. Several representative numerical experiments are carried out to illustrate and compare the performance of different proposed schemes.