稀疏微波成像回波数据可以建模为Toeplitz矩阵与地面场景的乘积，Toeplitz矩阵中的行向量为发射信号的时延。由于难于验证Toeplitz矩阵是否符合经典的稀疏信号处理中RIP等重建条件，因而分析稀疏微波成像采样数与发射波形的关系十分困难。近年提出的RIPless理论表明如果矩阵的行向量是对一个概率分布的随机抽取，并且该概率分布满足一定的条件，那么可以从少量的采样数据中恢复稀疏信号。Toeplitz矩阵适用于RIPless理论。该文首先介绍稀疏微波成像中观测矩阵的构造，然后利用稀疏信号处理中的RIPless理论分析波形中信号脉宽、带宽和信号形式与稀疏微波成像采样数的关系，进而比较不同波形对稀疏微波成像中的性能，最后通过仿真验证了该方法的有效性。%Echo data can be modeled as the product of the Toeplitz matrix and reflectivity of the observed scene. The row of the Toeplitz matrix is the time shift of the transmitted signal. Because it is difficult to verify whether the Toeplitz matrix satisfies the reconstruction condition (such as restricted isometry property) of sparse microwave imaging, analyzing the performance of the transmitted signal in sparse microwave imaging is a problem. RIPless, a new progress in sparse signal processing, shows that if the row of the matrix is an independent and identically distributed (i.i.d.) random vector drawn from a distribution, and this distribution satisfies certain conditions, then one can faithfully recover approximately sparse signals from a minimal number of measurements. The Toeplitz matrix satisfies RIPless. In this paper, we introduce the construction of the measurement matrix in sparse microwave imaging. Further, the relationship between pulse duration, bandwidth and waveform type, and the number of measurements in sparse microwave imaging are analyzed. The simulation results show the effectiveness of the proposed method.
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