Krylov methods in time‐reversal imaging by multiple‐signal‐classification.

Abstract

Multiple signal classification (MUSIC) has been used to form images and identify sound sources since 1986 [R. O. Schmidt, “Multiple emitter location and signal parameter estimation,” IEEE Trans. Antennas Propag., AP‐34, 276–280 (1986)]. In active sonar imaging of point targets, the MUSIC method can be used to estimate the range of the time‐reversal operator. In this context, the method is related to the decomposition of the time‐reversal operator method. Typical implementations of these methods utilize measurements of the entire time‐reversal operator, and require computations of its eigenvalues and eigenvectors. By contrast, we show that Krylov iterative methods can be used to perform MUSIC imaging with relatively few acoustic excitations. Furthermore, by using the Lanczos technique, no eigenvalues or eigenvectors need be computed. Rather, an orthonormal basis for the range space of the time‐reversal operator can be constructed directly from the received data. Most of the necessary computing is performed by the array itself, performing as a kind of “analog computer.” Finally, we show that useful images can be formed from one iteration to the next, while the data are being collected.