针对空空时间反转多信号分类（time reversal multiple signal classification，TR-MUSIC）抗噪性能差而难以实现对复杂随机介质影响下目标的聚焦成像，以及空空多态数据矩阵的获取较为复杂等问题，提出基于空频分解的时间反转成像新方法，即空频TR-MUSIC。该方法利用天线阵列采集的散射场回波信号建立空频多态数据矩阵，对该矩阵进行奇异值分解得到噪声子空间向量，从而实现对目标的成像。基于完全散射场数据的成像函数包含多个子矩阵的贡献，具有统计特性。仿真结果表明，无论是在自由空间中还是在随机介质背景下，空频TR-MUSIC的成像效果均优于传统的空空TR-MUSIC，具有较好的分辨率和定位精度。即使在信噪比为10 dB的高斯白噪声影响下，也能实现对目标的准确成像。
A time reversal imaging algorithm, based on the space-frequency decomposition, namely space-frequency TR-MUSIC, is proposed in an attempt to improve the focusing of the target obscured by complex random media, where TR-MUSIC algorithm may perform poorly when the signal to noise ratio (SNR) is low and the acquisition of the space-space multistatic data matrix (SS-MDM) is difficult. Using the backscattered data collected by an antenna array, a space-frequency multistatic data matrix (SF-MDM) is configured. Then the singular value decomposition is applied to the matrix to obtain the noisy subspace vector, which is then employed to image the target. The imaging function based on the full backscattered data includes the contributions of multiple sub-matrix and is found to be statistically stable. Numerical simulations show that the imaging performance of the space-frequency TR-MUSIC is better than that of the traditional space-space TR-MUSIC in both free space and random media, with fine resolution and good geometric accuracy under SNR as low as 10 dB.
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