There have been many approaches to estimating target location using seismic, ultrasonic, and electromagnetic imaging methods. Some of the most popular ones in recent years continue to be matched-field processing (Bucker, 1976; Jensen et al., 1994), MUSIC (MUltiple SIgnal Classification) (Schmidt, 1979; Johnson, 1982; Schmidt, 1986; Biondi and Kostov, 1989), and other linear subspace methods (Johnson, 1982; Johnson and DeGraaf, 1982; Cheney, 2001). When the targets are imbedded in heterogeneous media so that significant multiple scattering occurs in the background medium during wave propagation between array and target, the randomness has a different character than that usually envisioned in these traditional analyses. Yet there are a great many applications (Fink, 1997; 1999; Fink et al., 2000; Fink, 2001; Fink and Prada, 2001; ter Haar, 2001) ranging from the biomedical to ocean acoustics to nondestructive evaluation, where imaging is important and where sources of randomness not associated with the imaging targets can wreak havoc with the traditional methods. Time-reversal acoustics (Fink et al., 1989; Jackson and Dowling, 1991; Prada and Fink, 1991) offers part of the answer to these difficult imaging questions, and some significant improvements over these methods for imaging in random media are summarized here.
We have found that methods designed to work well for finding targets in homogeneous media do not necessarily work very well for targets imbedded in random media. In particular, the fact that the linear subspace methods are normally applied in the frequency domain combined with the fact that statistically stable methods are normally found only in the time domain, forces us to seek different imaging strategies in the random media imaging problems of interest to us here. We find that a set of imaging functionals having the desired characteristics exists, and furthermore that the properties of this set can be completely understood when the time-domain self-averaging -- that gives rise to the required statistical stability of the target images -- is taken properly into account. We can largely eliminate the undesirable features of the frequency domain methods by making a transform back to the time domain after first diagonalizing sensor array data. While the frequency domain analysis takes optimum advantage of eigenfunction orthogonality of the array data, a transform to the time-domain takes optimum advantage of wave self-averaging which then leads to the statistical stability we require for reliable and repeatable imaging in random media.
We first introduce the imaging problem in the next section. Then we summarize our technical approach. Examples of the cross-range (or bearing) estimates obtained with these methods are presented and then combined with range information from time-delay data to obtain our best estimates and images of target location. The final section summarizes our conclusions about the methods discussed.