Tradeoff of Computational Complexity and Accuracy in Space–Frequency Time Reversal Imaging

Time reversal (TR) has much potential to be used in more intelligent imaging applications. Developed with the TR imaging system of the large-scale array and wide bandwidth, the large elements and high sampling frequencies jointly increase the computational complexity significantly. Meanwhile, the weakened imaging accuracy is always accompanied on account of the reduced computations. To balance the computational complexity and imaging accuracy, this article proposes the optimal truncated space-frequency multiple signal classification (OTSF-MUSIC) imaging method. In this approach, the principal components of space-frequency multistatic data matrix (SF-MDM) are first obtained by the optimal truncated space-frequency (OTSF) operator. Second, the orthogonality between the SF-MDM and the noise space decomposed by the singular value decomposition (SVD) is demonstrated. Finally, the equivalent noise subspace constructed by the OTSF operator, which is proved to be also orthogonal to the SF-MDM, can be used in OTSF-MUSIC. The numerical results show that the proposed OTSF-MUSIC without SVD can save approximately 91% of runtimes and decline the imaging errors of 0.62<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda_{{\mathrm {c}}}$ </tex-math></inline-formula> at the extremely strong perturbated conditions, which indicates that OTSF-MUSIC achieves a tradeoff between the computational complexity and imaging accuracy.