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02151304 Berryman, James G. Borcea, Liliana Papanicolaou, George C. Tsogka, Chrysoula Statistical stability and time-reversal imaging in random media. Croke, Christopher B. (ed.) et al., Geometric methods in inverse problems and PDE control. Selected articles presented at the 2001 IMA summer program, Minneapolis, MN, USA. New York, NY: Springer (ISBN 0-387-40529-1/hbk). The IMA Volumes in Mathematics and its Applications 137, 15-24 (2003). 2003 New York, NY: Springer EN Localization of targets imbedded in a heterogeneous background medium is a common problem in seismic, ultrasonic, and electromagnetic imaging problems. The best imaging techniques make direct use of the eigenfunctions and eigenvalues of the array response matrix, as recent work on time-reversal acoustics has shown. Of the various imaging functionals studied, one that is representative of a preferred class is a time-domain generalization of MUSIC (MUltiple SIgnal Classification), which is a well-known linear subspace method normally applied only in the frequency domain. Since statistical stability is not characteristic of the frequency domain, a transform back to the time domain after first diagonalizing the array data in the frequency domain takes optimum advantage of both the time-domain stability and the frequency-domain orthogonality of the relevant eigenfunctions.