Structure analysis of single- and multi-frequency subspace migrations in inverse scattering problems

TL;DR

This paper investigates the structure of imaging functions in inverse scattering, revealing their relationship with Bessel functions and explaining how multi-frequency approaches improve imaging performance, supported by numerical simulations.

Contribution

It establishes a novel relationship between imaging functions and Bessel functions, explaining the enhancement from multi-frequency data in inverse scattering.

Findings

Imaging functions relate to Bessel functions.

Multi-frequency data improves imaging quality.

Numerical simulations validate theoretical insights.

Abstract

In this literature, we carefully investigate the structure of single- and multi-frequency imaging functions, that are usually employed in inverse scattering problems. Based on patterns of the singular vectors of the Multi-Static Response (MSR) matrix, we establish a relationship between imaging functions and the Bessel function. This relationship indicates certain properties of imaging functions and the reason behind enhancement in the imaging performance by multiple frequencies. Several numerical simulations with a large amount of noisy data are performed in order to support our investigation.