Singular value distribution of the propagation matrix in random scattering media

TL;DR

This study analyzes the singular value distribution of the propagation matrix in random media using ultrasonic experiments, comparing results with random matrix theory to understand scattering regimes and target detection.

Contribution

It provides experimental validation of singular value distributions in different scattering regimes and explores target detection based on singular value statistics.

Findings

Mean singular value distribution differs in single and multiple scattering regimes

Experimental results align well with random matrix theory predictions after normalization

Residual correlations between matrix elements influence scattering behavior

Abstract

The distribution of singular values of the propagation operator in a random medium is investigated, in a backscattering configuration. Experiments are carried out with pulsed ultrasonic waves around 3 MHz, using an array of 64 programmable transducers placed in front of a random scattering medium. The impulse responses between each pair of transducers are measured and form the response matrix. The evolution of its singular values with time and frequency is computed by means of a short-time Fourier analysis. The mean distribution of singular values exhibits very different behaviours in the single and multiple scattering regimes. The results are compared with random matrix theory. Once the experimental matrix coefficients are renormalized, experimental results and theoretical predictions are found to be in a very good agreement. Two kinds of random media have been investigated: a highly scattering medium in which multiple scattering predominates and a weakly scattering medium. In both cases, residual correlations that may exist between matrix elements are shown to be a key parameter. Finally, the possibility of detecting a target embedded in a random scattering medium based on the statistical properties of the strongest singular value is discussed.