Estimation of coherent scattering in dynamic random media

We address the question of estimating coherent scattering (weak scattering or coherent scatterer) by a time-evolving random medium. We consider two models of coherent scattering: homodyned K (HK) and generalized K (GK), and in both cases we derive stochastic differential equations for the scattered field. Approximate transition probabilities are computed using Euler-Maruyama scheme and the parameters for coherent scattering are estimated by maximum likelihood (ML). Using numerical simulations, we show that in the HK case, maximum likelihood estimation does not provide a significant advantage over a simplistic estimator based on the ergodicity property of the scattered field. On contrary, in GK scattering the transition probabilities carry significant information about the parameters, resulting in much better performance of the ML estimator.