One class of imaging methods available for time-reversal imaging of
small targets may be called linear subspace methods, of which the
best known method is probably MUSIC
(Schmidt, 1979; Marple, 1987; Stoica and Nehoral, 1990; Xu and Kaveh, 1996;
Stoica and Moses, 1997). The term MUSIC stands for
MUltiple SIgnal Classification scheme. The method determines whether
or not each vector in a set of vectors is fully or only partially in the
range of an operator. If is the operator of interest (*i.e.*, the time-reversal operator), and
the complete set of eigenvectors in the range of the operator (*i.e.*,
having nonzero eigenvalue) is given by , then we can choose
a test vector [see (Hr)] and define the square of the
direction
cosine between and any one eigenvector to be

^2(**V**_n,**H**_r) = **V**_n^*T**H**_r^2/**H**_r^2.
We are assuming in this formula that all the eigenvectors are
normalized so ,while is not necessarily normalized.

9/18/2001