Stability estimates of inverse random source problems for the wave equations by using correlation-based data

TL;DR

This paper establishes optimal Lipschitz stability estimates for inverse random source problems across various wave equations using correlation data from far-field patterns, advancing the understanding of stochastic inverse problems.

Contribution

It provides a unified framework demonstrating that correlation-based data can achieve optimal stability estimates for inverse problems in multiple wave equations.

Findings

Achieves Lipschitz-type stability estimates for inverse stochastic wave problems.

Unifies stability analysis across polyharmonic, electromagnetic, and elastic waves.

Uses correlation of far-field data at a single frequency for source reconstruction.

Abstract

This paper focuses on stability estimates of the inverse random source problems for the polyharmonic, electromagnetic, and elastic wave equations. The source is represented as a microlocally isotropic Gaussian random field, which is defined by its covariance operator in the form of a classical pseudo-differential operator. The inverse problem is to determine the strength function of the principal symbol by exploiting the correlation of far-field patterns associated with the stochastic wave equations at a single frequency. For the first time, we show in a unified framework that the optimal Lipschitz-type stability can be attained across all the considered wave equations through the utilization of correlation-based data.