Abstract
Considered here is a minimum mean square error (MMSE) estimator of a broadband acoustic response function over a vertical aperture based on an adaptive sparsity prior. The prior is a hierarchical Gaussian mixture distribution built on the assumption that acoustic paths can be partitioned into a relatively coherent set of arrivals that on average exhibit Doppler spreading about a mean rate and a set of incoherent paths that exhibit a flat Doppler spectra. The hierarchy establishes constraints on the parameters of each of these Gaussian models such that coherent components of the response are both sparse and in the ensemble obey the Doppler spread profile. An empirical Bayes approach is developed to estimate the latent parameters of the hierarchy, from which the shared time varying dilation process can ameliorated thereby enhancing coherent multi-path combining. The model is tested with acoustic communication recordings taken in shallow water at very low signal-to-noise ratios.