The compressive sensing theory enables reconstruction of sparse or compressible signals at reduced sampling rate. Recent studies have shown that stable signal reconstruction is possible even if each measurement is quantized to one bit. In conventional compressive sensing framework, the signal can be sparsely represented by some discrete atoms. In many applications however, signals are sparse in a continuous parameter space, e.g., radar imaging. A commonly used method is to discretize the continuous parameter into grid points and build a dictionary to characterize the sparsity. However, the true targets may not coincide with the predefined grid points. This off-grid problem always leads to a mismatched basis matrix, which results in degradation of the performance. In this paper, a parameter perturbation method, based on 1-bit compressive sensing is proposed to deal with the off-grid problem. Especially for adjacent targets in the adjoining grids, a self-checking mechanism is proposed to further discriminate the adjacent targets located within the proximity of adjoining grids. In the proposed algorithm, the available grid points in the dictionary are adaptively updated to approach the true targets. The convergence of the algorithm can be theoretically guaranteed, and numerical experiments demonstrate that the proposed algorithm can be effectively applied to range profile and synthetic aperture radar imaging. Simulations indicate that the proposed algorithm outperforms the state-of-the-art techniques over a wide range of signal-to-noise ratio levels.

压缩感测理论使得能够以降低的采样率重建稀疏或可压缩信号。最近的研究表明，即使每次测量量化为一位，也可以进行稳定的信号重建。在传统的压缩感测框架中，信号可以由一些离散的原子稀疏表示。但是，在许多应用中，信号在连续参数空间（例如，雷达成像）中稀疏。一种常用的方法是将连续参数离散化为网格点，并建立字典来表征稀疏性。但是，真实目标可能与预定义的网格点不一致。离网问题总是导致基矩阵不匹配，从而导致性能下降。本文采用参数摄动法 为了解决离网问题，提出了基于1位压缩感知的方法。特别是对于相邻网格中的相邻目标，提出了一种自检机制，以进一步区分位于相邻网格附近的相邻目标。在提出的算法中，字典中的可用网格点会自适应更新以逼近真实目标。理论上可以保证算法的收敛性，数值实验表明该算法可以有效地应用于测距和合成孔径雷达成像。仿真表明，在广泛的信噪比水平范围内，该算法优于最新技术。提出了一种自我检查机制，以进一步区分位于相邻网格附近的相邻目标。在提出的算法中，字典中的可用网格点会自适应更新以逼近真实目标。理论上可以保证算法的收敛性，数值实验表明该算法可以有效地应用于测距和合成孔径雷达成像。仿真表明，在广泛的信噪比水平范围内，该算法优于最新技术。提出了一种自我检查机制，以进一步区分位于相邻网格附近的相邻目标。在提出的算法中，字典中的可用网格点会自适应更新以逼近真实目标。理论上可以保证算法的收敛性，数值实验表明该算法可以有效地应用于测距和合成孔径雷达成像。仿真表明，在广泛的信噪比水平范围内，该算法优于最新技术。字典中的可用网格点将进行自适应更新，以逼近真实目标。理论上可以保证算法的收敛性，数值实验表明该算法可以有效地应用于测距和合成孔径雷达成像。仿真表明，在广泛的信噪比水平范围内，该算法优于最新技术。字典中的可用网格点将进行自适应更新，以逼近真实目标。理论上可以保证算法的收敛性，数值实验表明该算法可以有效地应用于测距和合成孔径雷达成像。仿真表明，在广泛的信噪比水平范围内，该算法优于最新技术。