Statistical stability in time reversal

TL;DR

This paper investigates how time reversal in wave propagation can achieve super-resolution and statistical stability in inhomogeneous media, especially under high-frequency and broadband conditions, using phase space analysis.

Contribution

It demonstrates that multiple scattering can enhance resolution beyond diffraction limits and establishes conditions for statistical stability of time reversal signals in complex media.

Findings

Super-resolution is achievable due to multiple scattering effects.

Time reversal signals are statistically stable for narrow-band sources.

Broad-band signals require spatially distributed sources for self-averaging.

Abstract

When a signal is emitted from a source, recorded by an array of transducers, time reversed and re-emitted into the medium, it will refocus approximately on the source location. We analyze the refocusing resolution in a high frequency, remote sensing regime, and show that, because of multiple scattering, in an inhomogeneous or random medium it can improve beyond the diffraction limit. We also show that the back-propagated signal from a spatially localized narrow-band source is self-averaging, or statistically stable, and relate this to the self-averaging properties of functionals of the Wigner distribution in phase space. Time reversal from spatially distributed sources is self-averaging only for broad-band signals. The array of transducers operates in a remote-sensing regime so we analyze time reversal with the parabolic or paraxial wave equation.