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^*TH_r^2/H_r^2. We are assuming in this formula that all the eigenvectors are normalized so ,while is not necessarily normalized.