Imaging and time reversal in random media

Abstract

We present a general method for estimating the location of small, well-separatedscatterers in a randomly inhomogeneous environment using an activesensor array. The main features of this method are (i) an arrival timeanalysis (ATA) of the echo received from the scatterers, (ii) a singular valuedecomposition of the array response matrix in the frequency domain,and (iii) the construction of an objective function in the time domainthat is statistically stable and peaks on the scatterers. By statisticallystable we mean here that the objective function is self-averaging overindividual realizations of the medium. This is a new approach to arrayimaging that is motivated by time reversal in random media, analysed indetail previously. It combines features from seismic imaging, like ATA,with frequency-domain signal subspace methodology like multiple signalclassification. We illustrate the theory with numerical simulations for ultrasound.