基于LBI的二维复稀疏信号重建算法及应用研究

陈文峰; 李少东; 杨军

doi:10.16383/j.aas.2016.c140897

基于LBI的二维复稀疏信号重建算法及应用研究

doi: 10.16383/j.aas.2016.c140897

空军预警学院武汉 430019

基金项目:

国家自然科学基金 61179014

详细信息

作者简介:
李少东, 空军预警学院博士研究生.2012年获得空军预警学院硕士学位. 主要研究方向为压缩感知, 逆合成孔径雷达成像.E-mail:liying198798@126.com

杨军, 空军预警学院副教授.2003年获得空军工程大学博士学位. 主要研究方向为雷达系统, 雷达成像, 压缩感知.E-mail:yangjem@126.com

通讯作者:
陈文峰, 空军预警学院博士研究生.2014年获得空军预警学院硕士学位. 主要研究方向为压缩感知, 逆合成孔径雷达成像.E-mail:chenwf925@163.com

计量
- 文章访问数: 1593
- HTML全文浏览量: 294
- PDF下载量: 728
- 被引次数: 0
出版历程
- 收稿日期: 2014-12-25
- 录用日期: 2015-12-07
- 刊出日期: 2016-04-01

2D Complex Sparse Reconstruction Algorithm with LBI and Its Application

Air Force Early Warning Academy, Wuhan 430019

Funds:

National Natural Science Foundation of China 61179014

More Information

Author Bio:
Ph. D. candidate at the Air Force Early Warning Academy. He received his master degree from Air Force Early Warning Academy in 2012. His research interest covers compressed sensing and inverse synthetic aperture radar imaging.

Associate professor at the Air Force Early Warning Academy. He received his Ph. D. degree from Air Force Engineering University in 2003. His research interest covers radar system, radar imaging, and compressed sensing.

Corresponding author: CHEN Wen-Feng Ph. D. candi- date at the Air Force Early Warning Academy. He received his master de- gree from Air Force Early Warning Academy in 2014. His research interest covers compressed sensing and inverse syn- thetic aperture radar imaging. Corresponding author of this paper.

摘要

摘要: 针对二维复稀疏信号重建时存在存储空间和计算复杂度增加的问题, 本文提出了一种快速并行重建二维复稀疏信号的并行线性Bregman迭代(Parallel fast linearized Bregman iteration, PFLBI)算法. 首先, 构建了二维复稀疏信号的结构模型以及PFLBI算法基本迭代格式; 其次, 通过变步长方式提高迭代收敛速度, 而每次迭代的步长则是通过估计中间变量的积累量突破收缩阈值需要的积累步数得到的; 再次, 对算法的性能指标进行了分析; 最后, 将该算法应用于逆合成孔径雷达(Inverse synthetic aperture radar, ISAR)成像. 实验结果表明该算法在重建性能和速度上具有优势.
- 稀疏重建 /
- 二维信号处理 /
- 线性Bregman迭代 /
- ISAR 成像
Abstract: A parallel fast linearized Bregman iteration (PFLBI) algorithm is proposed to solve the problem of large storage and complex computation in the reconstruction of 2D sparse signal. The PFLBI algorithm can efficiently reconstruct 2D sparse signal in a parallel way. Firstly, the matrix form of linearized Bregman iteration (LBI) is constructed. Secondly, the convergence speed is improved by estimating the number of the steps for intermediate variables to cross the shrinkage threshold. Thirdly, the performance of the proposed algorithm is analyzed. Finally, PFLBI is applied to inverse synthetic aperture radar (ISAR) imaging. Experimental results show that the proposed algorithm can improve the performance and the speed of reconstruction.
- Sparse reconstruction /
- 2D signal processing /
- linearized Bregman iteration (LBI) /
- inverse synthetic aperture radar (ISAR) imaging

HTML全文

图 1 任意稀疏结构二维复稀疏信号示意图

Fig. 1 The illustration of the 2D complex sparse signal

下载: 全尺寸图片幻灯片

图 2 本文算法重建结果

Fig. 2 Reconstruction results by the proposed algorithm

下载: 全尺寸图片幻灯片

图 3 算法收敛性验证

Fig. 3 算法收敛性验证

下载: 全尺寸图片幻灯片

图 4 相对重建误差与信噪比的关系

Fig. 4 Relationship between relative reconstruction error and SNR

下载: 全尺寸图片幻灯片

图 5 不同算法运算时间比较

Fig. 5 Comparison of CPU time of di®erent algorithms

下载: 全尺寸图片幻灯片

图 6 目标模型及脉压后结果

Fig. 6 目标模型及脉压后结果

下载: 全尺寸图片幻灯片

图 7 不同信噪比仿真数据成像结果

Fig. 7 Images under di®erent SNR by simulation data

下载: 全尺寸图片幻灯片

图 8 实测数据脉压后不同信噪比回波结果

Fig. 8 实测数据脉压后不同信噪比回波结果

下载: 全尺寸图片幻灯片

图 9 实测数据脉压后不同信噪比回波结果

Fig. 9 Images under di®erent SNR by real data

下载: 全尺寸图片幻灯片

参考文献(27)

[1]	Donoho D L. Compressed sensing. IEEE Transactions on Information Theory, 2006, 52(4): 1289-1306 doi: 10.1109/TIT.2006.871582
[2]	荆楠, 毕卫红, 胡正平, 王林. 动态压缩感知综述. 自动化学报, 2015, 41(1): 22-37 http://www.aas.net.cn/CN/abstract/abstract18580.shtml Jing Nan, Bi Wei-Hong, Hu Zheng-Ping, Wang Lin. A survey on dynamic compressed sensing. Acta Automatica Sinica, 2015, 41(1): 22-37 http://www.aas.net.cn/CN/abstract/abstract18580.shtml
[3]	沈燕飞, 李锦涛, 朱珍民, 张勇东, 代锋. 基于非局部相似模型的压缩感知图像恢复算法. 自动化学报, 2015, 41(2): 261-272 http://www.aas.net.cn/CN/abstract/abstract18605.shtml Shen Yan-Fei, Li Jin-Tao, Zhu Zhen-Min, Zhang Yong-Dong, Dai Feng. Image reconstruction algorithm of compressed sensing based on nonlocal similarity model. Acta Automatica Sinica, 2015, 41(2): 261-272 http://www.aas.net.cn/CN/abstract/abstract18605.shtml
[4]	张文林, 牛铜, 屈丹, 李弼程, 裴喜龙. 基于声学特征空间非线性流形结构的语音识别声学模型. 自动化学报, 2015, 41(5): 1024-1033 http://www.aas.net.cn/CN/abstract/abstract18676.shtml Zhang Wen-Lin, Niu Tong, Qu Dan, Li Bi-Cheng, Pei Xi-Long. Feature space nonlinear manifold based acoustic model for speech recognition. Acta Automatica Sinica, 2015, 41(5): 1024-1033 http://www.aas.net.cn/CN/abstract/abstract18676.shtml
[5]	方标, 黄高明, 高俊. LFM 宽带雷达信号的多通道盲压缩感知模型研究. 自动化学报, 2015, 41(3): 591-600 http://www.aas.net.cn/CN/abstract/abstract18636.shtml Fang Biao, Huang Gao-Ming, Gao Jun. A multichannel blind compressed sensing framework for linear frequency modulated wideband radar signals. Acta Automatica Sinica, 2015, 41(3): 591-600 http://www.aas.net.cn/CN/abstract/abstract18636.shtml
[6]	Massa A, Rocca P, Oliveri G. Compressive sensing in electromagnetics-a review. IEEE Antennas and Propagation Magazine, 2015, 57(1): 224-238 doi: 10.1109/MAP.2015.2397092
[7]	伍政华, 王强, 刘劼, 孙明建, 沈毅. 基于边膨胀图的压缩感知理论. 自动化学报, 2014, 40(12): 2824-2835 http://www.aas.net.cn/CN/abstract/abstract18561.shtml Wu Zheng-Hua, Wang Qiang, Liu Jie, Sun Ming-Jian, Shen Yi. Compressive sensing theory based on edge expander graphs. Acta Automatica Sinica, 2014, 40(12): 2824-2835 http://www.aas.net.cn/CN/abstract/abstract18561.shtml
[8]	Yu S W, Khwaja A S, Ma J W. Compressed sensing of complex-valued data. Signal Processing, 2011, 92(7): 357-362 http://cn.bing.com/academic/profile?id=2092062581&encoded=0&v=paper_preview&mkt=zh-cn
[9]	He Z Q, Shi Z P, Huang L, So H C. Underdetermined DOA estimation for wideband signals using robust sparse covariance fitting. IEEE Signal Processing Letters, 2015, 22(4): 435-439 doi: 10.1109/LSP.2014.2358084
[10]	Ender J H G. On compressive sensing applied to radar. Signal Processing, 2010, 90(5): 1402-1414 doi: 10.1016/j.sigpro.2009.11.009
[11]	Dong X, Zhang Y H. A novel compressive sensing algorithm for SAR imaging. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2014, 7(2): 708-720 doi: 10.1109/JSTARS.2013.2291578
[12]	Xu G, Xing M D, Bao Z. High-resolution inverse synthetic aperture radar imaging of manoeuvring targets with sparse aperture. Electronics Letters, 2015, 51(3): 287-289 doi: 10.1049/el.2014.3368
[13]	Yang Y, Liu F, Xu W L, Crozier S. Compressed sensing MRI via two-stage reconstruction. IEEE Transactions on biomedical engineering, 2015, 62(1): 110-118 doi: 10.1109/TBME.2014.2341621
[14]	Duarte M F, Baraniuk R G. Kronecker compressive sensing. IEEE Transactions on Image Processing, 2012, 21(2): 494-504 doi: 10.1109/TIP.2011.2165289
[15]	Gan L. Block compressed sensing of natural images. In: Proceedings of the 15th International Conference on Digital Signal Processing. Cardiff, UK: IEEE, 2007. 403-406 http://www.oalib.com/references/19339271
[16]	Cotter S F, Rao B D, Engan K, Kreutz-Delgado K. Sparse solutions to linear inverse problems with multiple measurement vectors. IEEE Transactions on Signal Processing, 2005, 53(7): 2477-2488 doi: 10.1109/TSP.2005.849172
[17]	Hao F, Vorobyov S A, Hai J, Taheri O. Permutation meets parallel compressed sensing: how to relax restricted isometry property for 2D sparse signals. IEEE Transactions on Signal Processing, 2014, 62(1): 196-210 doi: 10.1109/TSP.2013.2284762
[18]	Duarte M F, Eldar Y C. Structured compressed sensing: from theory to applications. IEEE Transactions on Signal Processing, 2011, 59(9): 4053-4085 doi: 10.1109/TSP.2011.2161982
[19]	Tropp J A. Algorithms for simultaneous sparse approximation. Part II: convex relaxation. Signal Processing, 2006, 86(3): 589-602
[20]	张贤达. 矩阵分析与应用. 第2版. 北京: 清华大学出版社, 2013. 32-35 Zhang Xian-Da. Matrix Analysis and Applications (2nd edition). Beijing: Tsinghua University Press, 2013. 32-35
[21]	Erdogan A T, Kizilkale C. Fast and low complexity blind equalization via subgradient projections. IEEE Transactions on Signal Processing, 2005, 53(7): 2513-2524 doi: 10.1109/TSP.2005.849195
[22]	Bregman L M. The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming. USSR Computational Mathematics and Mathematical Physics, 1967, 7(3): 200-217 doi: 10.1016/0041-5553(67)90040-7
[23]	Osher S, Mao Y, Dong B, Yin W. Fast linearized Bregman iteration for compressive sensing and sparse denoising. Communications in Mathematical Sciences, 2011, 8(1): 93-111 http://cn.bing.com/academic/profile?id=2061315188&encoded=0&v=paper_preview&mkt=zh-cn
[24]	Cai J F, Osher S, Shen Z W. Linearized Bregman iterations for frame-based image deblurring. SIAM Journal on Imaging Sciences, 2009, 2(1): 226-252 doi: 10.1137/080733371
[25]	Yin W, Osher S, Goldfarb D, Darbon J. Bregman iterative algorithms for l₁-minimization with applications to compressed sensing. SIAM Journal on Imaging Sciences, 2008, 1(1): 143-168 doi: 10.1137/070703983
[26]	李少东, 杨军, 马晓岩. 基于压缩感知的ISAR高分辨成像算法. 通信学报, 2013, 34(9): 150-157 http://www.cnki.com.cn/Article/CJFDTOTAL-TXXB201309018.htm Li Shao-Dong, Yang Jun, Ma Xiao-Yan. High resolution ISAR imaging algorithm based on compressive sensing. Journal on Communications, 2013, 34(9): 150-157 http://www.cnki.com.cn/Article/CJFDTOTAL-TXXB201309018.htm
[27]	Zhang S H, Zhang W, Zong Z L, Tian Z, Yeo T S. High-resolution bistatic ISAR imaging based on two-dimensional compressed sensing. IEEE Transactions on Antennas and Propagation, 2015, 63(5): 2098-2111 doi: 10.1109/TAP.2015.2408337