Low Complexity Time Reversal Imaging Methods Based on Truncated Time Reversal Operator

Due to the spatiotemporal focusing property of the time reversal (TR) technique, the TR operator (TRO)-based imaging method offers favorable positioning accuracy and fine distinguishability. However, the conventional singular value decomposition (SVD) for the full TRO involves significant computational complexity in large-scale arrays. To reduce the large computational complexity, this article proposes a truncated TRO (TTRO)-based imaging method that eliminates the need for SVD. In the approach, the TTRO is constructed by a block matrix from the TRO to reduce dimensionality, which reduces the complexity of decomposing the full TRO. Then, the quadrature rectangle decomposition (QRD) is employed to decompose the TTRO instead of the full TRO to acquire the signal subspace and noise subspace. Based on different subspaces, the TTRO-based imaging method can be classified into the decomposition of the TTRO (DORTT) using the signal subspace and the TTRO-multiple signal classification (TTRO-MUSIC) using the noise subspace. Numerical results demonstrate that the proposed TTRO-based method significantly decreases computational complexity and saves approximately 95% of the runtime consumption compared to the conventional TRO-based imaging method. Moreover, compared to the derived propagator method-multiple signal classification (PM-MUSIC) with the estimated noise subspace, TTRO-MUSIC also provides lower computational complexity and achieves better positioning accuracy.