矩阵信息几何中值检测器

华小强; 程永强; 王宏强; 王勇献; 张理论

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矩阵信息几何中值检测器

更新时间：2022-02-08

- 矩阵信息几何中值检测器
- Matrix Information Geometric Median Detectors
- 电子学报 2022年页码：1-11
- 作者机构：
  
  1.国防科技大学气象海洋学院，湖南长沙 410079
  2.国防科技大学电子科学学院，湖南长沙 410079
- 作者简介：
  
  [ "华小强男，1990年生，湖北黄冈人，讲师，主要研究方向为信息几何、信号检测、海洋信息融合.E-mail:hxq712@yeah.net" ]
  [ "程永强（通信作者）男，1982年生，河北张家口人，教授，主要研究方向为雷达目标检测、雷达前视成像、信息几何.E-mail:nudtyqcheng@gmail.com" ]
- 基金信息：
  
  国家自然科学基金(61901479)
- DOI：
  中图分类号： TN911.23;TN911.72
- 收稿：2020-07-09，
  
  修回：2021-08-24，
  
  网络出版：2022-02-08，
- 稿件说明：
移动端阅览
华小强, 程永强, 王宏强, 等. 矩阵信息几何中值检测器[J/OL]. 电子学报, 2022,1-11.

Xiao-qiang HUA, Yong-qiang CHENG, Hong-qiang WANG, et al. Matrix Information Geometric Median Detectors[J/OL]. ACTA ELECTRONICA SINICA, 2022, 1-11.
华小强, 程永强, 王宏强, 等. 矩阵信息几何中值检测器[J/OL]. 电子学报, 2022,1-11. DOI：

Xiao-qiang HUA, Yong-qiang CHENG, Hong-qiang WANG, et al. Matrix Information Geometric Median Detectors[J/OL]. ACTA ELECTRONICA SINICA, 2022, 1-11. DOI：

摘要

本文以矩阵信息几何理论为基础，提出一种新的信号检测器框架，该检测器将样本数据建模为正定矩阵，利用参考单元对应正定矩阵的几何中值来估计杂波协方差矩阵，从而将信号检测问题转化为度量矩阵流形上两点间的差异性大小，通过比较流形上两点间的差异值与阈值大小来实现信号检测.此外，深入分析了流形上不同几何度量所反映出的几何结构差异，并依据各向异性定义了几何度量的区分能力描述子.由于几何度量的区分性较好，并且几何中值对干扰具有较好的鲁棒性，因此，矩阵信息几何中值检测器在小样本、非均匀环境下具有较好的性能.实验结果表明，与自适应匹配滤波相比，所提出的信号检测器在小样本、非均匀环境下具有明显的性能优势.

Abstract

This paper systematically summarizes the previous work

and proposes a new signal detector in the framework of matrix information geometry theory. The sample data is modeled as a hermitian positive definite (HPD) matrix

and a set of secondary HPD matrices is used for estimating the clutter covariance matrix by the geometric median. Then

the problem of signal detection is treated as discriminating two points on the HPD manifold

and signal detection is realized by comparing the difference between the two points with a given threshold. In addition

we analyze the differences in geometric structure that is reflected by different geometric measures on manifolds. The discrimination ability descriptor of a geometric measure is defined based on the anisotropy. Since the geometric measures are more discriminative and their corresponding medians are robust to the interference

matrix information geometric median detectors can exhibit well performances. Experimental results confirm the advantages of the proposed geometric median detectors in comparison with the adaptive matched filtering in nonhomogeneous environments with limited sample data.

关键词

Keywords

references

KELLY E J . An adaptive detection algorithm [J]. IEEE Transactions on Aerospace and Electronic Systems , 1986 , AES- 22 ( 2 ): 115 - 127 .

ROBEY F C , FUHRMANN D R , KELLY E J , et al . A CFAR adaptive matched filter detector [J]. IEEE Transactions on Aerospace and Electronic Systems , 1992 , 28 ( 1 ): 208 - 216 .

GINI F , GIANNAKIS G B , GRECO M , et al . Time-averaged subspace methods for radar clutter texture retrieval [J]. IEEE Transactions on Signal Processing , 2001 , 49 ( 9 ): 1886 - 1898 .

孟祥伟 . 量化秩非参数CFAR检测器在杂波边缘中的性能分析 [J]. 电子学报 , 2020 , 48 ( 2 ): 384 - 389 .

MENG X W . Performance analysis of rank quantization nonparametric CFAR detector at clutter edge [J]. Acta Electronica Sinica , 2020 , 48 ( 2 ): 384 - 389 . (in Chinese)

LI H , JIANG Y , FANG J , et al . Adaptive subspace signal detection with uncertain partial prior knowledge [J]. IEEE Transactions on Signal Processing , 2017 , 65 ( 16 ): 4394 - 4405 .

MAIO A D , FARINA A , FOGLIA G . Design and experimental validation of knowledge-based constant false alarm rate detectors [J]. IET Radar , Sonar & Navigation, 2007 , 1 ( 4 ): 308 - 316 .

AUBRY A , CAROTENUTO V , MAIO A D , et al . Exploiting multiple a priori spectral models for adaptive radar detectio [J]. IET Radar , Sonar & Navigation, 2014 , 8 ( 7 ): 695 - 707 .

SOLOVEYCHIK I , WIESEL A . Joint estimation of inverse covariance matrices lying in an unknown subspace [J]. IEEE Transactions on Signal Processing , 2017 , 65 ( 9 ): 2379 - 2388 .

MAIO A D , FARINA A , FOGLIA G . Knowledge-aided Bayesian radar detectors & their application to live data [J]. IEEE Transactions on Aerospace and Electronic Systems , 2010 , 46 ( 1 ): 170 - 183 .

WANG P , LI H , HIMED B . Knowledge-aided parametric tests for multichannel adaptive signal detection [J]. IEEE Transactions on Signal Processing , 2011 , 59 ( 12 ): 5970 - 5982 .

WIESEL A , BIBI O , GLBERSON A . Time varying autoregressive moving average models for covariance estimation [J]. IEEE Transactions on Signal Processing , 2013 , 61 ( 11 ): 2791 - 2801 .

BIDON S , LASSERRE M , CHEVALIER F L . Unambiguous sparse recovery of migrating targets with a robustified Bayesian model [J]. IEEE Transactions on Aerospace and Electronic Systems , 2019 , 55 ( 1 ): 108 - 123 .

LAPUYADE-LAHORGUE J , BARBARESCO F . Radar detection using Siegel distance between autoregressive processes, application to HF and X-band radar [C]// 2008 IEEE Radar Conference . Rome, Italy : IEEE , 2008 : 1 - 6 .

ARNAUDON M , BARBARESCO F , YANG L . Riemannian medians and means with applications to radar signal processing [J]. IEEE Journal of Selected Topics in Signal Processing , 2013 , 7 ( 4 ): 595 - 604 .

BARBARESCO F . Innovative tools for radar signal processing based on Cartan's geometry of SPD matrices & Information Geometry [C]// 2008 IEEE Radar Conference . Rome, Italy : IEEE , 2008 : 1 - 6 .

LIU Z , BARBARESCO F . Doppler information geometry for wake turbulence monitoring [M]//Nielsen F, Bhatia R. Matrix Information Geometry . Berlin, Heidelberg : Springer Berlin Heidelberg , 2013 : 277 - 290 .

BARBARESCO F , MEIER U . Radar monitoring of a wake vortex: Electromagnetic reflection of wake turbulence in clear air [J]. Comptes Rendus Physique , 2010 , 11 ( 1 ): 54 - 67 .

HUA X Q , CHENG Y Q , WANG H Q , et al . Geometric means and medians with applications to target detection [J]. IET Signal Processing , 2017 , 11 ( 6 ): 711 - 720 .

HUA X Q , CHENG Y Q , WANG H Q , et al . Matrix CFAR detectors based on symmetrized Kullback-Leibler and total Kullback-Leibler divergences [J]. Digital Signal Processing , 2017 , 69 : 106 - 116 .

HUA X Q , CHENG Y Q , WANG H Q , et al . Geometric target detection based on total Bregman divergence [J]. Digital Signal Processing , 2018 , 75 : 232 - 241 .

HUA X Q , CHENG Y Q , WANG H Q , et al . Information geometry for covariance estimation in heterogeneous clutter with total Bregman divergence [J]. Entropy , 2018 , 20 ( 4 ): 258 .

HUA X Q , FAN H Y , CHENG Y Q , et al . Information geometry for radar target detection with total Jensen-Bregman divergence [J]. Entropy , 2018 , 20 ( 4 ): 256 .

HUA X Q , CHENG Y Q , WANG H Q , et al . Robust covariance estimators based on information divergences and Riemannian manifold [J]. Entropy , 2018 , 20 ( 4 ): 219 .

HUA X Q , SHI Y F , ZENG Y , et al . A divergence mean-based geometric detector with a pre-processing procedure [J]. Measurement , 2019 , 131 : 640 - 646 .

HUA X Q , CHENG Y Q , LI Y B , et al . A divergence median-based geometric detector with a weighted averaging filter [J]. Journal of Physics: Conference Series , 2018 , 960 : 012045 .

HUA X Q , CHENG Y Q , LI Y B , et al . Target detection in sea clutter via weighted averaging filter on the Riemannian manifold [J]. Aerospace Science and Technology , 2017 , 70 : 47 - 54 .

HUA X Q , CHENG Y Q , LI Y B , et al . A extended matrix CFAR detector with a pre-processing procedure [C]// 2017 10th International Congress on Image and Signal Processing, BioMedical Engineering and Informatics (CISP-BMEI) . Shanghai : IEEE , 2017 : 1 - 6 .

黎湘 , 程永强 , 王宏强 , 等 . 信息几何理论与应用研究进展 [J]. 中国科学(信息科学) , 2013 , 43 ( 6 ): 707 - 732 .

LI X , CHENG Y Q , WANG H Q , et al . Progress in theory and applications of information geometry [J]. Science China (Information Sciences) , 2013 , 43 ( 6 ): 707 - 732 . (in Chinese)

华小强 . 基于矩阵信息几何的雷达目标检测方法研究 [D]. 长沙 : 国防科学技术大学 , 2018 .

HUA X Q . Research on radar target detection method based on matrix information geometry [D]. Changsha : National University of Defense Techno- logy , 2018 . (in Chinese)

孙华飞 , 彭林玉 , 张真宁 . 信息几何及其应用 [J]. 数学进展 , 2011 , 40 ( 3 ): 257 - 269 .

SUN H F , PENG L Y , ZHANG Z N . Information geometry and its applications [J]. Advances In Mathematics , 2011 , 40 ( 3 ): 257 - 269 . (in Chinese)

华小强 . 基于信息几何的图像目标识别关键技术研究 [D]. 长沙 : 国防科学技术大学 , 2014 .

HUA X Q . Research on key technologies of image object recognition based on information geometry [D]. Changsha : National University of Defense Technology , 2014 . (in Chinese)

华小强 , 王平 , 高颖慧等 . 基于信息几何的图像去噪 [J]. 计算机工程与科学 , 2015 , 37 ( 3 ): 589 - 593 .

HUA X Q , WANG P , GAO Y H , et al . Image denoising based on information geometry [J]. Computer Engineering and Science , 2015 , 37 ( 3 ): 589 - 593 . (in Chinese)

程永强 . 雷达信号处理的信息理论与几何方法研究 [D]. 长沙 : 国防科学技术大学 , 2012 .

CHENG Y Q . Information theory and geometric methods of radar signal processing [D]. Changsha : National University of Defense Technology , 2012 . (in Chinese)

赵兴刚 , 郑岱堃 , 王首勇等 . 一种基于AR模型的矩阵CFAR检测器 [J]. 电子学报 , 2017 , 45 ( 12 ): 3019 - 3024 .

ZHAO X G , ZHENG D K , WANG S Y , et al . A matrix CFAR detector based on AR model [J]. Acta Electronica Sinica , 2017 , 45 ( 12 ): 3019 - 3024 . (in Chinese)

赵文静 , 金明录 , 刘文龙 . 基于谱范数的矩阵CFAR检测器 [J]. 电子学报 , 2019 , 47 ( 9 ): 1951 - 1956 .

ZHAO W J , JIN M L , LIU W L . Matrix CFAR detector based on matrix spectral norm [J]. Acta Electronica Sinica , 2019 , 47 ( 9 ): 1951 - 1956 . (in Chinese)

赵兴刚 , 王首勇 , 郑岱堃 . 一种基于信息几何的矩阵DP-TBD算法 [J]. 电子学报 , 2017 , 45 ( 4 ): 882 - 889 .

ZHAO X G , WANG S Y , ZHENG D K . A matrix DP-TBD algorithm based on information geometry [J]. Acta Electronica Sinica , 2017 , 45 ( 4 ): 882 - 889 . (in Chinese)

MOAKHER M . A differential geometric approach to the geometric mean of symmetric positive-definite matrices [J]. SIAM J Matrix Anal Appl , 2005 , 26 ( 3 ): 735 - 747 .

MOAKHER M . On the averaging of symmetric positive-definite tensors [J]. Journal of Elasticity , 2006 , 82 ( 3 ): 273 - 296 .

ARSIGNY V , FILLARD P , PENNEC X , et al . Log-Euclidean metrics for fast and simple calculus on diffusion tensors [J]. Magnetic Resonance in Medicine , 2006 , 56 ( 2 ): 411 - 421 .

MOAKHER M , BATCHELOR P G . Symmetric positive-definite matrices: From geometry to applications and visualization [M]//Weickert J, Hagen H. Visualization and Processing of Tensor Fields . Berlin, Heidelberg : Springer Berlin Heidelberg . 2006 : 285 - 298 .

MOAKHER M . Divergence measures and means of symmetric positive-definite matrices [C]// New Developments in the Visualization and Processing of Tensor Fields . Berlin Heidelberg : Springer , 2012 : 307 - 321 .

FLETCHER P T , VENKATASUBRAMANIAN S , JOSHI S . Robust statistics on Riemannian manifolds via the geometric median [C]// 2008 IEEE Conference on Computer Vision and Pattern Recognition . Anchorage, USA : IEEE . 2008 : 1 - 8 .

ARSIGNY V , FILLARD P , PENNEC X , et al . Geometric means in a novel vector space structure on symmetric positive-definite matrices [J]. SIAM Journal on Matrix Analysis and Applications , 2007 , 29 ( 1 ): 328 - 347 .

CHARFI M , CHEBBI Z , MOAKHER M , et al . Bhattacharyya median of symmetric positive-definite matrices and application to the denoising of diffusion-tensor fields [J]. Proc IEEE Int Symp Biomed Imaging , 2013 : 1227 - 1230 .

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