Complex 1-bit Compressive Sensing for SAR Imaging Based on Inverse Chirp Scaling Algorithm

The compressive sensing framework aims to stably recover sparse signals at reduced sampling rate. Recent research has shown that only the sign information of the measurements can achieve accurate signal recovery. Most work focused on the real-valued signals. In many applications, however, the signals are complex-valued. Also, the existing reconstruction algorithms always involve large matrix-vector multiplications which make them more time and memory consuming than traditional matched filtering-based methods. In this paper, we propose a 1-bit compressive sensing reconstruction algorithm for recovering complex sparse signals using approximated observation matrix which is deduced from the inverse of chirp-scaling method. This algorithm directly operates on complex data and greatly reduce the computation time and memory usage. Both simulated and real data validate the efficiency of the proposed algorithm.