低信噪比下二维联合快速超分辨B-ISAR成像方法
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摘要
双基地ISAR成像分辨率受限于信号带宽和方位积累时间,且成像质量受噪声影响严重.本文在充分考虑回波的二维联合稀疏特征基础上,提出二维联合字典下的矩阵复数近似消息传递超分辨快速成像算法.在构建双基地ISAR的二维联合超分辨成像模型基础上,首先通过向量化处理,将二维超分辨成像问题转换为复数基追踪去噪问题;其次通过两种策略实现复数基追踪去噪问题的快速求解,一是利用向量化与Kronecker积的关系,推导出矩阵形式复数近似消息传递算法,从而避免向量化处理带来的大矩阵运算量和大存储量问题;二是为进一步减少单次迭代的运算量,将矩阵乘法等效为二维快速傅里叶变换.最后,利用本文算法在迭代过程中对噪声阈值不断精确逼近,提高算法在低信噪比下的成像能力.仿真数据成像结果验证了本文算法的有效性.
In B-ISAR imaging, the range resolution and cross-range resolution are dependent on the signal band and the coherent processing interval, respectively. Generally, the B-ISAR image is seriously affected by noise. In this paper,a matrix form of complex approximate message passing algorithm based on two dimensional coupled dictionaries( MCAMP-TCD) is presented,by considering the 2D coupling sparse feature of the echo. Firstly, the range-azimuth 2D joint B-ISAR imaging model is established. Then the 2D joint super-resolution imaging problem is converted into a complex basis pursuit denoising( C-BPDN) problem through vectorization operation. Secondly, two strategies are implemented to solve C-BPDN problem quickly, the first strategy is utilizing the relation between vectorization operation and Kronecker product to derivate the matrix form of complex approximate message passing algorithm,which can avoid the high computational complexity and memory requirements due to vectorization operation. In second strategy, the two dimensional fast Fourier transform( 2D FFT) is introduced to equivalent matrix multiplication,which further reduces the computational complexity of the single iteration. At last, the imaging capability under low signal to noise ratio( SNR) is improved by the ability to accurately approximate the noise threshold of the MCAMP-TCD. Simulation results verify the effectiveness of the proposed method.
In B-ISAR imaging, the range resolution and cross-range resolution are dependent on the signal band and the coherent processing interval, respectively. Generally, the B-ISAR image is seriously affected by noise. In this paper,a matrix form of complex approximate message passing algorithm based on two dimensional coupled dictionaries( MCAMP-TCD) is presented,by considering the 2D coupling sparse feature of the echo. Firstly, the range-azimuth 2D joint B-ISAR imaging model is established. Then the 2D joint super-resolution imaging problem is converted into a complex basis pursuit denoising( C-BPDN) problem through vectorization operation. Secondly, two strategies are implemented to solve C-BPDN problem quickly, the first strategy is utilizing the relation between vectorization operation and Kronecker product to derivate the matrix form of complex approximate message passing algorithm,which can avoid the high computational complexity and memory requirements due to vectorization operation. In second strategy, the two dimensional fast Fourier transform( 2D FFT) is introduced to equivalent matrix multiplication,which further reduces the computational complexity of the single iteration. At last, the imaging capability under low signal to noise ratio( SNR) is improved by the ability to accurately approximate the noise threshold of the MCAMP-TCD. Simulation results verify the effectiveness of the proposed method.
引文
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[15]张龙,张磊,邢孟道.一种基于改进压缩感知的低信噪比ISAR高分辨成像方法[J].电子与信息学报,2010,32(9):2263-2267.ZHANG Long,ZHANG Lei,XING M eng-dao.A new method of high resolution ISAR imaging under low SNR based on improved compressive sensing[J].Journal of Electronics&Information Technology,2010,32(9):2263-2267.(in Chinese)
[16]李少东,陈文峰,杨军,等.任意稀疏结构的多量测向量快速稀疏重构方法研究[J].电子学报,2015,43(4):708-715.LI Shao-dong,CHEN Wen-feng,YANG Jun,et al.Study on the fast sparse recovery algorithm via multiple measurement vectors of arbitrary sparse structure[J].Acta Electronica Sinica,2015,43(4):708-715.(in Chinese)
[17]王天云,陆新飞,丁丽,等.基于贝叶斯压缩感知的FDM IM O雷达OFF-Grid目标稀疏成像[J].电子学报,2016,44(6):1314-1321.WANG Tian-yun,LU Xin-fei,DING Li,et al.Bayesian compressive sensing-based sparse imaging for off-grid target in frequency diverse M IM O radar[J].Acta Electronica Sinica,2016,44(6):1314-1321.(in Chinese)
[18]MALEKI A,et al.Asymptotic analysis of complex LASSO via complex approximate message passing[J].IEEE Transactions on Information Theory,2013,59(7):4290
[19]朱仁飞,罗迎,张群,等.双基地ISAR成像分析[J].现代雷达,2011,33(8):33-38.ZHU Ren-fei,LUO Ying,ZHANG Qun,et al.Analysis of bistatic inverse synthetic aperture radar imaging[J].M odern Radar,2011,33(8):33-38.(in Chinese)
[20]张贤达.矩阵分析与应用[M].北京:清华大学出版社,2013.ZHANG Xian-da.M atrix Analysis and Applications[M].Beijing:Tsinghua University Press,2013.(in Chinese)
[21]MALEKI A.Approximate message passing algorithm for compressed sensing[D].Stanford University,2011.
[22]DONOHO D L,MALEKI A,MONTANARI A.Message passing algorithms for compressed sensing[J].Proceedings of the National Academy of the Sciences of the United States of America,2009,106(45):18914-18919.
[23]YANG J,ZHANG Y.Alternating direction algorithms for L1-problems in compressive sensing[J].SIAM Journal on Scientific Computing,2011,33(1):250-278.
[24]张磊.高分辨SAR/ISAR成像及误差补偿技术研究[D].西安:西安电子科技大学,2012.ZHANG Lei.Study on high resolution SAR/ISAR imaging and error correction[D].Xi’an:Xidian University,2012.(in Chinese)
[2]CHEN V C,ROSIERS A D,LIPPS R.Bi-static ISAR range-Doppler imaging and resolution analysis[A].2009IEEE Radar Conference[C].California:Pasadena,2009.1-5.
[3]艾小峰,邹小海,李浩智,等.T/R-R双基地雷达进动目标参数估计与ISAR成像[J].电子学报,2012,40(6):1148-1153.AI Xiao-feng,ZOU Xiao-hai,LI Hao-zhi,et al.Parameter estimation and ISAR imaging of precession targets using T/R-R bistatic radars[J].Acta Electronica Sinica,2012,40(6):1148-1153.(in Chinese)
[4]ZHANG Shun-sheng,SUN Si-bo,ZHANG Wei,et al.High-resolution bistatic ISAR image formation for highspeed and complex-motion targets[J].IEEE Journal of Selected Topics in Applied Earth Observation and Remote Sensing,2015,8(7):3520-3531.
[5]郭宝锋,尚朝轩,王俊岭,等.双基地角时变下的逆合成孔径雷达越分辨单元徙动校正算法[J].物理学报,2014,63(23):238406.Guo Bao-feng,Shang Chao-xuan,Wang Jun-ling,et al.Correction of migration through resolution cell in bistatic inverse synthetic aperture radar in the presence of time-varying bistatic angle[J].Acta Physica Sinica,2014,63(23):238406.(in Chinese)
[6]张龙,苏涛,刘峥,等.双基地雷达两极区ISAR超分辨成像[J].光子学报,2015,44(3):0328002.ZHANG Long,SU Tao,LIU Zheng,et al.Super resolution ISAR imaging in receiver centered region area in bistatic[J].Acta Photonica Sinica,2015,44(3):0328002.(in Chinese)
[7]柴守刚,陈卫东,陈畅.联合几何畸变校正及定标的BISAR稀疏成像算法[J].现代雷达,2015,32(1):32-37.CHAI Shou-gang,CHEN Wei-dong,CHEN Chang.BISAR sparse imaging algorithm w ith geometric distortion correction and calibration[J].M odern Radar,2015,32(1):32-37.(in Chinese)
[8]ZHANG Shun-sheng,ZHANG Wei,ZONG Zhu-lin,et al.High-resolution bistatic ISAR imaging based on tw o-dimensional compressed sensing[J].IEEE Transactions on Antennas and Propagation,2015,63(5):2098-2111.
[9]李少东,陈文峰,杨军,等.低信噪比下的二维联合线性布雷格曼迭代快速超分辨成像算法[J].物理学报,2016,65(3):038401.LI Shao-dong,CHEN Wen-feng,YANG Jun,et al.A fast tw o dimensional joint linearized bregman iteration algorithm for super-resolution inverse synthetic aperture radar imaging at low signal-to-noise ratios[J].Acta Physica Sinica,2016,65(3):038401.(in Chinese)
[10]韩宁,尚朝轩,董健,等.小转角下空间目标双基地ISAR二维成像算法[J].传感器与微系统,2011,30(11):138-141.HAN Ning,SHANG Chao-xuan,DONG Jian,et al.2D imaging algorithm for bistatic ISAR of space target in small rotating angle[J].Transducer and M icrosystem Technologies,2011,30(11):138-141.(in Chinese)
[11]DONOHO D L.Compressed sensing[J].IEEE Transactions on Information Theory,2006,52(4):1289-1306.
[12]韩宁,刘伟,何强,等.稀疏正则化在双基地ISAR距离成像中的应用[J].现代雷达,2012,34(4):24-27.HAN Ning,LIU Wei,HE Qiang,et al.Application of sparse regularization in bistatic ISAR range profile imaging[J].M odern Radar,2012,34(4):24-27.(in Chinese)
[13]LIU Zhen,WEI Xi-zhang,LI Xiang.Decoupled ISAR imaging using RSFW based on tw ice compressed sensing[J].IEEE Transactions on Aerospace and Electronic Systems,2014,50(4):3195–3211.
[14]吴敏,邢孟道,张磊.基于压缩感知的二维联合超分辨ISAR成像算法[J].电子与信息学报,2014,36(1):187-193.WU M in,XING M eng-dao,ZHANG Lei.Tw o dimensional joint super-resolution ISAR imaging algorithm based on compressive sensing[J].Journal of Electronics&Information Technology,2014,36(1):187-193.(in Chinese)
[15]张龙,张磊,邢孟道.一种基于改进压缩感知的低信噪比ISAR高分辨成像方法[J].电子与信息学报,2010,32(9):2263-2267.ZHANG Long,ZHANG Lei,XING M eng-dao.A new method of high resolution ISAR imaging under low SNR based on improved compressive sensing[J].Journal of Electronics&Information Technology,2010,32(9):2263-2267.(in Chinese)
[16]李少东,陈文峰,杨军,等.任意稀疏结构的多量测向量快速稀疏重构方法研究[J].电子学报,2015,43(4):708-715.LI Shao-dong,CHEN Wen-feng,YANG Jun,et al.Study on the fast sparse recovery algorithm via multiple measurement vectors of arbitrary sparse structure[J].Acta Electronica Sinica,2015,43(4):708-715.(in Chinese)
[17]王天云,陆新飞,丁丽,等.基于贝叶斯压缩感知的FDM IM O雷达OFF-Grid目标稀疏成像[J].电子学报,2016,44(6):1314-1321.WANG Tian-yun,LU Xin-fei,DING Li,et al.Bayesian compressive sensing-based sparse imaging for off-grid target in frequency diverse M IM O radar[J].Acta Electronica Sinica,2016,44(6):1314-1321.(in Chinese)
[18]MALEKI A,et al.Asymptotic analysis of complex LASSO via complex approximate message passing[J].IEEE Transactions on Information Theory,2013,59(7):4290
[19]朱仁飞,罗迎,张群,等.双基地ISAR成像分析[J].现代雷达,2011,33(8):33-38.ZHU Ren-fei,LUO Ying,ZHANG Qun,et al.Analysis of bistatic inverse synthetic aperture radar imaging[J].M odern Radar,2011,33(8):33-38.(in Chinese)
[20]张贤达.矩阵分析与应用[M].北京:清华大学出版社,2013.ZHANG Xian-da.M atrix Analysis and Applications[M].Beijing:Tsinghua University Press,2013.(in Chinese)
[21]MALEKI A.Approximate message passing algorithm for compressed sensing[D].Stanford University,2011.
[22]DONOHO D L,MALEKI A,MONTANARI A.Message passing algorithms for compressed sensing[J].Proceedings of the National Academy of the Sciences of the United States of America,2009,106(45):18914-18919.
[23]YANG J,ZHANG Y.Alternating direction algorithms for L1-problems in compressive sensing[J].SIAM Journal on Scientific Computing,2011,33(1):250-278.
[24]张磊.高分辨SAR/ISAR成像及误差补偿技术研究[D].西安:西安电子科技大学,2012.ZHANG Lei.Study on high resolution SAR/ISAR imaging and error correction[D].Xi’an:Xidian University,2012.(in Chinese)