针对实际逆合成孔径雷达(ISAR)成像时带宽有限、方位孔径稀疏的小角度回波数据条件下，常规算法的成像分辨率不高等问题，基于压缩感知理论，提出了一种低信噪比条件下的二维联合布雷格曼迭代快速ISAR超分辨成像算法。首先，将雷达回波构建为距离频域-方位多普勒域的二维稀疏表示模型，在此基础上，将二维超分辨成像问题转换为二维联合压缩感知的稀疏重构问题；其次，为了避免重构时向量化操作带来的复杂度，提出了二维联合布雷格曼迭代算法，为实现快速重构，将加权残量迭代、估计停滞步长与感知矩阵条件数优化三种加快收敛速度的思想相结合，既利用了布雷格曼迭代在低信噪比条件下的重构能力又能保证快速成像。最后仿真实验结果表明在欠采样和低信噪比条件下本文算法能够缩短成像时间，且具备更好的噪声鲁棒性。%In practical inverse synthetic aperture radar (ISAR), the traditional imaging algorithms have low range and low cross-range resolutions while the echoes have limited bandwidth and sparse azimuth aperture in small coherent processing interval. To obtain super-resolution ISAR imaging at low signal-to-noise (SNR) ratios, this paper puts forward a novel fast two-dimensional joint linearized Bregman iteration (2D-JLBI) algorithm based on compressive sensing theory. Firstly, the radar echoes are established as a two-dimensional joint sparse representation model in the range frequency-azimuth Doppler domain. Consequently, the original two-dimensional super resolution imaging problem is converted into a two-dimensional jointly compressive reconstruction problem. Secondly, to avoid the reconstruction complexity from the vectorization of the echoes, the two-dimensional joint linearized Bregman iterative algorithm is proposed. Meanwhile, three strategies, namely the weighted residual iteration, estimation of the stagnation step, and optimizing the condition numbers of sensing matrices, are combined to improve the convergence speed. Both the ISAR imaging ability at low SNR and its speed are improved obviously. Finally, simulation experiments show that the proposed algorithm can shorten the imaging time and have better noise robustness under the condition of sub-Nyquist sampling rate and low SNR.
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