A quantitative direct sampling method for inhomogeneities from multi-frequency backscattering measurements

TL;DR

This paper introduces a new direct sampling method for quantitatively reconstructing inhomogeneities from multi-frequency backscattering data, supported by theoretical proof and numerical validation.

Contribution

It advances inverse scattering theory by providing a local uniqueness proof and a novel, robust, and efficient quantitative reconstruction technique.

Findings

The method accurately reconstructs inhomogeneities in numerical experiments.

Numerical results demonstrate robustness and computational efficiency.

Theoretical proof of local uniqueness supports the method's validity.

Abstract

The inverse scattering problem from the multi-frequency backscattering data is a long-standing open problem. We advance the theory by proving a local uniqueness result. Moreover, we introduce a direct sampling method for quantitatively reconstructing unknown inhomogeneities. Comprehensive numerical experiments validate the robustness, accuracy, and computational effectiveness of the proposed quantitative direct sampling method.