High resolution population density imaging of random scatterers with the matched filtered scattered field variance

The matched filter enables imaging with high spatial resolution and high signal-to-noise ratio by coherent correlation with the expected field from what is assumed to be a discrete scatterer. In many physical imaging systems, however, returns from a large number of randomized scatterers, ranging from thousands to millions of individuals, are received together and the coherent or expected field vanishes. Despite this, it is shown that cross-spectral coherence in the matched filtered variance retains a pulse compression property that enables high-resolution imaging of scatterer population density. Analytic expressions for the statistical moments of the broadband matched filtered scattered field are derived in terms of the medium's Green's function, object scatter function, and spatial distribution using a single-scatter approximation. The formulation can account for potential dispersion in the medium and target over the signal bandwidth, and can be used to compare the relative levels of the coherent and incoherent scattered intensities. The analytic model is applied to investigate population density imaging of fish distributions in the Gulf of Maine with an ultrasonic echosounder. The results are verified with numerical Monte-Carlo simulations that include multiple scattering, illustrating that the single-scatter approximation is valid even for relatively dense Atlantic herring (Clupea harengus) schools.