  The wave propagation in random medium plays a critical role in optics and
quantum physics. Multiple scattering of coherent wave in a random medium
determines the transport procedure. Brownian motions of the scatterers perturb
each propagation trajectory and form dynamic speckle patterns in the
backscattered direction. In this study, we applied the random matrix theory
(RMT) to investigate the eigenvalue density of the backscattered intensity
matrix. We find that the dynamic speckle patterns can be utilized to decouple
the singly and multiply backscattered components. The Wishart random matrix of
multiple scattering component is well described by the Marcenko-Pastur law,
while the single scattering part has low-rank characteristic. We therefore
propose a strategy for estimating the first and the second order moments of
single and multiple scattering components, respectively, based on the
Marcenko-Pastur law and trace analysis. Electric field Monte Carlo simulation
and in-vivo experiments demonstrate its potential applications in hidden
absorbing object detection and in-vivo blood flow imaging. Our method can be
applied to other coherent domain elastic scattering phenomenon for wide-filed
propagation of microwave, ultrasound and etc.
