A quantitative study of source imaging in random waveguides

TL;DR

This paper investigates how boundary and medium perturbations in random waveguides affect source imaging, proposing adaptive filtering techniques to optimize image quality and discussing when incoherent methods are necessary.

Contribution

It provides a rigorous stochastic analysis of wave field behavior in perturbed waveguides and introduces adaptive filters to improve coherent imaging performance.

Findings

Boundary scattering can be mitigated with optimized filters.

Long-range medium scattering is harder to mitigate, requiring incoherent methods.

Adaptive filtering improves image quality in perturbed waveguides.

Abstract

We present a quantitative study of coherent array imaging of remote sources in randomly perturbed waveguides with bounded cross-section. We study how long range cumulative scattering by perturbations of the boundary and the medium impedes the imaging process. We show that boundary scattering effects can be mitigated with filters that enhance the coherent part of the data. The filters are obtained by optimizing a measure of quality of the image. The point is that there is an optimal trade-off between the robustness and resolution of images in such waveguides, which can be found adaptively, as the data are processed to form the image. Long range scattering by perturbations of the medium is harder to mitigate than scattering by randomly perturbed boundaries. Coherent imaging methods do not work and more complex incoherent methods, based on transport models of energy, should be used instead. Such methods are nor useful, nor needed in waveguides with perturbed boundaries. We explain all these facts using rigorous asymptotic stochastic analysis of the wave field in randomly perturbed waveguides. We also analyze the adaptive coherent imaging method and obtain a quantitative agreement with the results of numerical simulations.