可变先验贝叶斯学习稀疏SAR成像

doi:10.12305/j.issn.1001-506X.2021.07.07

摘要/Abstract

摘要：

针对合成孔径雷达(synthetic aperture radar, SAR)在稀疏成像中, 传统贝叶斯机器学习算法存在先验固化、成像结果容易过拟合等问题。提出一种可变成像先验贝叶斯(varying imaging prior Bayes, VIP-Bayes)学习稀疏SAR成像算法。首先, 引入可动态灵活表征目标散射特征的广义高斯分布先验。然后，在贝叶斯推理框架下进行分层建模, 后验分布推导。最后, 针对常规吉布斯采样算法无法采样复杂后验分布的问题, 引入哈密顿蒙特卡罗(Hamiltonian Monte Carlo, HMC)采样算法进行求解。另外, 考虑到HMC算法对非平滑后验分布无法采样，因此引入近端算子, 进行近端梯度近似, 提出近端-HMC(proximal-HMC, P-HMC)算法。P-HMC算法可有效解决非平滑后验采样问题。因而可实现VIP-Bayes稀疏成像。通过仿真数据进行算法有效性验证, 选取SAR实测数据与多种算法进行成像对比实验, 利用相变热力图对算法成像性能进行定量分析，验证了所提算法的实用性和优越性。

关键词: 合成孔径雷达, 贝叶斯学习, 哈密顿蒙特卡罗算法, 广义高斯分布

Abstract:

Aiming at the problem of prior solidification and over-fitting imaging results easily of traditional Bayesian learning imaging algorithms in sparse synthetic aperture radar (SAR) imagery, a varying imaging prior Bayes (VIP-Bayes) learning algorithm is proposed. Firstly, the generalized Gaussian distribution variable dynamic prior is introduced, which can realize the dynamic and flexible representation of the target scattering prior knowledge. Then, in the framework of Bayesian inference, a hierarchical Bayesian model is introduced to derive the posterior distribution. Finally, aiming at the problerm, which the conventional Gibbs algorithm cannot sample the obtained complicated posterior distribution, the Hamiltonian Monte Carlo (HMC) sampling algorithm is introduced to solve the problem. In addition, considering the HMC algorithm can't sample for non-smooth posterior distributions. This paper introduces a proximal operator to approximate the gradient, and obtains the proximal-HMC (P-HMC) sampling algorithm. P-HMC algorithm can effectively solve the problem of non-smooth posterior sampling, for this reason, it can realize sparse imaging based on VIP-Bayes learning. The effectiveness of the algorithm is verified by using the simulation data, then select SAR raw data to conduct a variety of algorithm imaging comparison experiments. Finally, phase transition diagram is applied to quantitatively analyze the algorithm imaging performance. In a word, all above experiments verifies the practicability and superiority of the proposed algorithm.

Key words: synthetic aperture radar (SAR), Bayes learning, Hamiltonian Monte Carlo (HMC) algorithm, generalized Gaussian distribution (GGD)

中图分类号:

TN957

沈笑云, 廖仙华, 孙卫天, 夏亚波, 杨磊. 可变先验贝叶斯学习稀疏SAR成像[J]. 系统工程与电子技术, 2021, 43(7): 1781-1790.

Xiaoyun SHEN, Xianhua LIAO, Weitian SUN, Yabo XIA, Lei YANG. Sparse SAR imaging based on varying prior Bayes learning[J]. Systems Engineering and Electronics, 2021, 43(7): 1781-1790.

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参考文献 31

1	张新征, 黄培康. 基于贝叶斯压缩感知的SAR目标识别[J]. 系统工程与电子技术, 2013, 35 (1): 40- 44. doi: 10.3969/j.issn.1001-506X.2013.01.07
	ZHANG X Z , HUANG P K . SAR ATR based on Bayesian compressive sensing[J]. Journal of Systems Engineering and Electronics, 2013, 35 (1): 40- 44. doi: 10.3969/j.issn.1001-506X.2013.01.07
2	DONOHO D L . Compressed sensing[J]. IEEE Trans.on Information Theory, 2006, 52 (4): 1289- 1306. doi: 10.1109/TIT.2006.871582
3	杨磊, 李慧娟, 黄博, 等. 双层稀疏组Lasso高分辨SAR结构特征增强成像[J]. 系统工程与电子技术, 2021, 43 (2): 351- 362.
	YANG L , LI H J , HUANG B , et al. High resolution SAR imagery with structural feature enhancement under two-layer sparse group Lasso[J]. Systems Engineering and Electronics, 2021, 43 (2): 351- 362.
4	YANG L , LI P C , ZHANG S , et al. Cooperative multitask learning for sparsity-driven SAR imagery and nonsystematic error autocalibration[J]. on Geoscience and Remote Sensing, 2020, 58 (7): 5132- 5143. doi: 10.1109/TGRS.2020.2972972
5	ZHOU D Y , YIN X Y , ZONG Z Y . Multi-trace basis-pursuit seismic inversion for resolution enhancement[J]. Geophysical Prospecting, 2019, 67 (3): 519- 531. doi: 10.1111/1365-2478.12752
6	CHEN S S , DONOHO D L , SAUNDERS M A . Atomic decomposition by basis pursuit[J]. SIAM Journal on Scientific Computing, 2001, 43 (1): 129- 159.
7	FIGUEIREDO M A T , NOWAK R D , WRIGHT S J . Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems[J]. IEEE Journal of Selected Topics in Signal Processing, 2008, 1 (4): 586- 597.
8	STEPHEN B , NEAL P , CHU E , et al. Distributed optimization and statistical learning via the alternating direction method of multipliers[M]. New York: Foundations and Trends in Machine Learning, 2011.
9	BABACAN S D , MOLINA R , KATSAGGELOS A K , et al. Bayesian compressive sensing using laplace priors[J]. on Image Process, 2010, 19 (1): 53- 63. doi: 10.1109/TIP.2009.2032894
10	WU Q , ZHANG Y D , AMIN M G , et al. High-resolution passive SAR imaging exploiting structured Bayesian compressive sensing[J]. IEEE Journal of Selected Topics in Signal Processing, 2015, 9 (8): 1484- 1497. doi: 10.1109/JSTSP.2015.2479190
11	NOGUEIRA F E A , MARQUES R C P , MEDEIROS F N S . SAR image segmentation based on unsupervised classification of log-cumulants estimates[J]. IEEE Geoscience and Remote Sensing Letters, 2020, 17 (7): 1287- 1289. doi: 10.1109/LGRS.2019.2941075
12	MORADIKIA M , SAMADI S , CETIN M . Joint SAR imaging and multi-feature decomposition from 2-D under-sampled data via low-rankness plus sparsity priors[J]. IEEE Trans.on Computational Imaging, 2019, 5 (1): 1- 16. doi: 10.1109/TCI.2018.2881530
13	BAI X R , ZHANG Y , ZHOU F . High-resolution radar imaging in complex environments based on Bayesian learning with mixture models[J]. IEEE Trans.on Geoscience and Remote Sensing, 2019, 57 (2): 972- 984. doi: 10.1109/TGRS.2018.2863743
14	YANG L , ZHAO L F , BI G A , et al. SAR ground moving target imaging algorithm based on parametric and dynamic sparse Bayesian learning[J]. IEEE Trans.on Geoscience and Remote Sensing, 2016, 54 (2): 2254- 2267.
15	WANG L , ZHAO L F , BI G A , et al. Enhanced ISAR imaging by exploiting the continuity of the target scene[J]. IEEE Trans.on Geoscience and Remote Sensing, 2014, 52 (9): 5736- 5750. doi: 10.1109/TGRS.2013.2292074
16	ZHAO N , BASARAB A , KOUAME D , et al. Joint segmentation and deconvolution of ultrasound images using a hierarchical Bayesian model based on generalized Gaussian priors[J]. IEEE Trans.on Image Process, 2014, 25 (8): 3304- 3319.
17	CHAARI L, TOURNERET J Y, CHAUX C. Sparse signal recovery using a Bernoulli generalized Gaussian prior[C]//Proc. of the 23rd European Signal Processing Conference, 2015.
18	ZHAO N, BASARAB A, KOUAME D, et al. Restoration of ultrasound images using a hierarchical Bayesian model with a generalized Gaussian prior[C]//Proc. of the IEEE International Conference on Image Processing, 2014.
19	ISWARAN H . Gibbs sampling methods for stick-breaking priors[J]. Journal of the American Statistical Association, 2001, 96 (453): 161- 173. doi: 10.1198/016214501750332758
20	CHAARI L , TOURNERET J , CHAUX C , et al. A Hamiltonian Monte Carlo method for non-smooth energy sampling[J]. IEEE Trans.on Signal Processing, 2016, 64 (21): 5585- 5594. doi: 10.1109/TSP.2016.2585120
21	NEAL R M . MCMC using Hamiltonian dynamics[J]. ArXiv: Computation, 2011, 21.
22	PEREYRA M . Proximal markov chain Monte Carlo algorithms[J]. Stats and Computing, 2016, 26 (4): 13- 34.
23	HOFFMAN M D , GELMAN A . The no-u-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo[J]. Journal of Machine Learning Research, 2011, 15 (1): 2320- 2335.
24	PARIKH N , BOYD S . Proximal algorithms[J]. Foundations and Trends in Optimization, 2013, 1 (3): 123- 231.
25	CORBINEAU M , KOUAMÉ D , CHOUZENOUX E , et al. Preconditioned P-ULA for joint deconvolution segmentation of ultrasound images[J]. IEEE Signal Processing Letters, 2019, 26 (10): 1456- 1460. doi: 10.1109/LSP.2019.2935610
26	COMBETTES P L , DUNG D , BNG C V . Proximity for sums of composite functions[J]. Journal of Mathematical Analysis & Applications, 2010, 380 (2): 680- 688.
27	徐志林, 魏中浩, 吴辰阳, 等. 基于l₁正则化的多通道滑动聚束SAR成像[J]. 系统工程与电子技术, 2019, 41 (2): 304- 310.
	XU Z L , WEI Z H , WU C Y , et al. Multichannel sliding spotlight SAR imaging based on l₁ regularization[J]. Systems Engineering and Electronics, 2019, 41 (2): 304- 310.
28	杨磊, 李埔丞, 李慧娟, 等. 稳健高效通用SAR图像稀疏特征增强算法[J]. 电子与信息学报, 2019, 41 (12): 2826- 2835. doi: 10.11999/JEIT190173
	YANG L , LI P C , LI H J , et al. Robust and efficient general SAR image sparse feature enhancement algorithm[J]. Journal of Electronics and Information Technology, 2019, 41 (12): 2826- 2835. doi: 10.11999/JEIT190173
29	YANG L , BI G A , XING M D , et al. Airborne SAR moving target signatures and imagery based on LVD[J]. IEEE Trans.on Geoscience and Remote Sensing, 2015, 53 (11): 5958- 5971. doi: 10.1109/TGRS.2015.2429678
30	田野, 毕辉, 张冰尘, 等. 相变图在稀疏微波成像变化检测降采样分析中的应用[J]. 电子与信息学报, 2015, 37 (10): 2335- 2341.
	TIAN Y , BI H , ZHANG B C , et al. Application of phase diagram to sampling ratio analysis in sparse microwave imaging change detection[J]. Journal of Electronics & Information Technology, 2015, 37 (10): 2335- 2341.
31	吴辰阳, 魏中浩, 张冰尘, 等. 基于复近似信息传递的多通道SAR成像方法[J]. 系统工程与电子技术, 2018, 40 (6): 1249- 1254.
	WU C Y , WEI Z H , ZHANG B C , et al. Multi-channel SAR imaging method based on CAMP[J]. Systems Engineering and Electronics, 2018, 40 (6): 1249- 1254.

项目	参数值
机载雷达高度/m	4 000
飞行速率/(m/s)	100
脉冲重复频率/Hz	100
脉冲宽度/μs	5
载波频率/GHz	10
发射信号带宽/MHz	150
天线方位向尺寸/m	1.7
距离向分辨率/m	1
方位向分辨率/m	0.85

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