Fast and Efficient Time-Reversal Imaging Using Space-Frequency Propagator Method

It is known that the eigenvalue decomposition and singular value decomposition (SVD) of multi-static data matrices (MDMs) are the basis of time-reversal (TR) imaging. However, the computational loads of the SVD can be significantly high when the MDMs are large. The computational cost of the propagator method (PM) without any SVD of MDMs is much lower than that of SVD-based methods. In this paper, to reduce the computational complexity in TR imaging, first a novel space-frequency propagator method (SF-PM) for TR imaging in large MDMs is proposed. The computational complexity of the proposed SF-PM is then analyzed. Moreover, the theoretical analysis is presented to show that the SF-PM has a significantly lower computational complexity than the conventional SVD-based approach. Finally, the reasonable imaging results and superior computational efficiency of the SF-PM are verified by simulation.