Energy and regularity dependent stability estimates for near-field inverse scattering in multidimensions

TL;DR

This paper establishes new stability estimates for near-field inverse scattering problems in multiple dimensions, showing improved stability with higher energy and regularity, and providing results for both 2D and higher dimensions.

Contribution

It introduces novel global H"older-logarithmic stability estimates for the inverse scattering problem, enhancing understanding of stability dependence on energy and regularity.

Findings

Stability estimates increase with energy and regularity

Provides stability estimates in dimensions d≥3 and d=2

Establishes global logarithmic stability in 2D

Abstract

We prove new global H\"older-logarithmic stability estimates for the near-field inverse scattering problem in dimension $d\geq 3$. Our estimates are given in uniform norm for coefficient difference and related stability efficiently increases with increasing energy and/or coefficient regularity. In addition, a global logarithmic stability estimate for this inverse problem in dimension $d=2$ is also given.