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

Random matrix description of dynamically backscattered coherent waves propagating in a wide-field-illuminated random medium