Stability estimate for an inverse problem for the time harmonic magnetic Schr\"odinger operator from the near and far field pattern

TL;DR

This paper establishes logarithmic stability estimates for recovering magnetic and electric potentials in a time harmonic magnetic Schrödinger inverse scattering problem using near and far field data, advancing theoretical understanding.

Contribution

It provides new logarithmic stability estimates for inverse magnetic Schrödinger problems, combining geometrical optics solutions with existing techniques.

Findings

Logarithmic stability estimates for potential recovery

Effective use of near and far field data

Extension of techniques to magnetic Schrödinger operators

Abstract

We derive conditional stability estimates for inverse scattering problems related to time harmonic magnetic Schr\"odinger equation. We prove logarithmic type estimates for retrieving the magnetic (up to a gradient) and electric potentials from near field or far field maps. Our approach combines techniques from similar results obtained in the literature for inhomogeneous inverse scattering problems based on the use of geometrical optics solutions.