One bit compressive sensing with off-grid targets

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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.