Imaging and time reversal in random media

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

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