Stability on the Inverse Random Source Scattering Problem for the One-Dimensional Helmholtz Equation

TL;DR

This paper investigates the stability of reconstructing the statistical properties of a random source in a 1D stochastic Helmholtz equation, demonstrating improved stability with multi-frequency boundary data.

Contribution

It provides a stability analysis for the inverse problem of determining the mean and variance of a random source, highlighting the benefits of multi-frequency data.

Findings

Stability improves with multi-frequency boundary data.

The inverse problem is solvable for the statistical properties of the source.

Using suitable boundary data enhances reconstruction accuracy.

Abstract

Consider the one-dimensional stochastic Helmholtz equation where the source is assumed to be driven by the white noise. This paper concerns the stability analysis of the inverse random source problem which is to reconstruct the statistical properties of the source such as the mean and variance. Our results show that increasing stability can be obtained for the inverse problem by using suitable boundary data with multi-frequencies.