Wave Propagation and Imaging in Random Media: From Gaussian to non-Gaussian statistics

Abstract: We consider wave propagation and imaging in random media with the aim to describe the wave statistics and to discuss correlation-based imaging. When scattering is strong enough the coherent (mean) wave vanishes and the second-order moments of the wave field (more exactly, the statistical Wigner transform) satisfies a radiative transfer equation. Under such circumstances the wave correlations or Wigner transform should be used for correlation-based imaging. In this talk we discuss the statistical stability of the empirical Wigner transform. We discuss two regimes with different behaviors. In the random paraxial regime the fluctuations of the smoothed Wigner transform are small and correlation-based imaging is possible. In randomly perturbed open waveguides the fluctuations of the mode powers and wave intensities grow exponentially and correlation-based imaging is challenging.

Mathematics

Audience: researchers in the topic

International Zoom Inverse Problems Seminar, UC Irvine