Information Geometry for Covariance Estimation in Heterogeneous Clutter with Total Bregman Divergence
This paper presents a covariance matrix estimation method based on information geometry in a heterogeneous clutter. In particular, the problem of covariance estimation is reformulated as the computation of geometric median for covariance matrices estimated by the secondary data set. A new class of t...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-04-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/20/4/258 |
| _version_ | 1828369171441778688 |
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| author | Xiaoqiang Hua Yongqiang Cheng Hongqiang Wang Yuliang Qin |
| author_facet | Xiaoqiang Hua Yongqiang Cheng Hongqiang Wang Yuliang Qin |
| author_sort | Xiaoqiang Hua |
| collection | DOAJ |
| description | This paper presents a covariance matrix estimation method based on information geometry in a heterogeneous clutter. In particular, the problem of covariance estimation is reformulated as the computation of geometric median for covariance matrices estimated by the secondary data set. A new class of total Bregman divergence is presented on the Riemanian manifold of Hermitian positive-definite (HPD) matrix, which is the foundation of information geometry. On the basis of this divergence, total Bregman divergence medians are derived instead of the sample covariance matrix (SCM) of the secondary data. Unlike the SCM, resorting to the knowledge of statistical characteristics of the sample data, the geometric structure of matrix space is considered in our proposed estimators, and then the performance can be improved in a heterogeneous clutter. At the analysis stage, numerical results are given to validate the detection performance of an adaptive normalized matched filter with our estimator compared with existing alternatives. |
| first_indexed | 2024-04-14T06:20:59Z |
| format | Article |
| id | doaj.art-e90cff0a643f493eaa66a289054bed41 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-14T06:20:59Z |
| publishDate | 2018-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-e90cff0a643f493eaa66a289054bed412022-12-22T02:08:03ZengMDPI AGEntropy1099-43002018-04-0120425810.3390/e20040258e20040258Information Geometry for Covariance Estimation in Heterogeneous Clutter with Total Bregman DivergenceXiaoqiang Hua0Yongqiang Cheng1Hongqiang Wang2Yuliang Qin3School of Electronic Science, National University of Defence Technology, Changsha 410073, ChinaSchool of Electronic Science, National University of Defence Technology, Changsha 410073, ChinaSchool of Electronic Science, National University of Defence Technology, Changsha 410073, ChinaSchool of Electronic Science, National University of Defence Technology, Changsha 410073, ChinaThis paper presents a covariance matrix estimation method based on information geometry in a heterogeneous clutter. In particular, the problem of covariance estimation is reformulated as the computation of geometric median for covariance matrices estimated by the secondary data set. A new class of total Bregman divergence is presented on the Riemanian manifold of Hermitian positive-definite (HPD) matrix, which is the foundation of information geometry. On the basis of this divergence, total Bregman divergence medians are derived instead of the sample covariance matrix (SCM) of the secondary data. Unlike the SCM, resorting to the knowledge of statistical characteristics of the sample data, the geometric structure of matrix space is considered in our proposed estimators, and then the performance can be improved in a heterogeneous clutter. At the analysis stage, numerical results are given to validate the detection performance of an adaptive normalized matched filter with our estimator compared with existing alternatives.http://www.mdpi.com/1099-4300/20/4/258covariance matrix estimationtotal Bregman divergenceinformation geometryadaptive normalized matched filter |
| spellingShingle | Xiaoqiang Hua Yongqiang Cheng Hongqiang Wang Yuliang Qin Information Geometry for Covariance Estimation in Heterogeneous Clutter with Total Bregman Divergence Entropy covariance matrix estimation total Bregman divergence information geometry adaptive normalized matched filter |
| title | Information Geometry for Covariance Estimation in Heterogeneous Clutter with Total Bregman Divergence |
| title_full | Information Geometry for Covariance Estimation in Heterogeneous Clutter with Total Bregman Divergence |
| title_fullStr | Information Geometry for Covariance Estimation in Heterogeneous Clutter with Total Bregman Divergence |
| title_full_unstemmed | Information Geometry for Covariance Estimation in Heterogeneous Clutter with Total Bregman Divergence |
| title_short | Information Geometry for Covariance Estimation in Heterogeneous Clutter with Total Bregman Divergence |
| title_sort | information geometry for covariance estimation in heterogeneous clutter with total bregman divergence |
| topic | covariance matrix estimation total Bregman divergence information geometry adaptive normalized matched filter |
| url | http://www.mdpi.com/1099-4300/20/4/258 |
| work_keys_str_mv | AT xiaoqianghua informationgeometryforcovarianceestimationinheterogeneousclutterwithtotalbregmandivergence AT yongqiangcheng informationgeometryforcovarianceestimationinheterogeneousclutterwithtotalbregmandivergence AT hongqiangwang informationgeometryforcovarianceestimationinheterogeneousclutterwithtotalbregmandivergence AT yuliangqin informationgeometryforcovarianceestimationinheterogeneousclutterwithtotalbregmandivergence |