Target Detection Using Nonsingular Approximations for a Singular Covariance Matrix
Accurate covariance matrix estimation for high-dimensional data can be a difficult problem. A good approximation of the covariance matrix needs in most cases a prohibitively large number of pixels, that is, pixels from a stationary section of the image whose number is greater than several times the...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Electrical and Computer Engineering |
| Online Access: | http://dx.doi.org/10.1155/2012/628479 |
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| _version_ | 1850159579865808896 |
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| author | Nir Gorelik Dan Blumberg Stanley R. Rotman Dirk Borghys |
| author_facet | Nir Gorelik Dan Blumberg Stanley R. Rotman Dirk Borghys |
| author_sort | Nir Gorelik |
| collection | DOAJ |
| description | Accurate covariance matrix estimation for high-dimensional data can be a difficult problem. A good approximation of the covariance matrix needs in most cases a prohibitively large number of pixels, that is, pixels from a stationary section of the image whose number is greater than several times the number of bands. Estimating the covariance matrix with a number of pixels that is on the order of the number of bands or less will cause not only a bad estimation of the covariance matrix but also a singular covariance matrix which cannot be inverted. In this paper we will investigate two methods to give a sufficient approximation for the covariance matrix while only using a small number of neighboring pixels. The first is the quasilocal covariance matrix (QLRX) that uses the variance of the global covariance instead of the variances that are too small and cause a singular covariance. The second method is sparse matrix transform (SMT) that performs a set of K-givens rotations to estimate the covariance matrix. We will compare results from target acquisition that are based on both of these methods. An improvement for the SMT algorithm is suggested. |
| format | Article |
| id | doaj-art-ae1f5ba1a31e440fa0ccf84edb0b46a9 |
| institution | OA Journals |
| issn | 2090-0147 2090-0155 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Electrical and Computer Engineering |
| spelling | doaj-art-ae1f5ba1a31e440fa0ccf84edb0b46a92025-08-20T02:23:28ZengWileyJournal of Electrical and Computer Engineering2090-01472090-01552012-01-01201210.1155/2012/628479628479Target Detection Using Nonsingular Approximations for a Singular Covariance MatrixNir Gorelik0Dan Blumberg1Stanley R. Rotman2Dirk Borghys3Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, IsraelDepartment of Geography and Environmental Development, Ben-Gurion University of the Negev, Beer-Sheva 84105, IsraelDepartment of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, IsraelSignal and Image Centre, Royal Military Academy, 1000 Brussels, BelgiumAccurate covariance matrix estimation for high-dimensional data can be a difficult problem. A good approximation of the covariance matrix needs in most cases a prohibitively large number of pixels, that is, pixels from a stationary section of the image whose number is greater than several times the number of bands. Estimating the covariance matrix with a number of pixels that is on the order of the number of bands or less will cause not only a bad estimation of the covariance matrix but also a singular covariance matrix which cannot be inverted. In this paper we will investigate two methods to give a sufficient approximation for the covariance matrix while only using a small number of neighboring pixels. The first is the quasilocal covariance matrix (QLRX) that uses the variance of the global covariance instead of the variances that are too small and cause a singular covariance. The second method is sparse matrix transform (SMT) that performs a set of K-givens rotations to estimate the covariance matrix. We will compare results from target acquisition that are based on both of these methods. An improvement for the SMT algorithm is suggested.http://dx.doi.org/10.1155/2012/628479 |
| spellingShingle | Nir Gorelik Dan Blumberg Stanley R. Rotman Dirk Borghys Target Detection Using Nonsingular Approximations for a Singular Covariance Matrix Journal of Electrical and Computer Engineering |
| title | Target Detection Using Nonsingular Approximations for a Singular Covariance Matrix |
| title_full | Target Detection Using Nonsingular Approximations for a Singular Covariance Matrix |
| title_fullStr | Target Detection Using Nonsingular Approximations for a Singular Covariance Matrix |
| title_full_unstemmed | Target Detection Using Nonsingular Approximations for a Singular Covariance Matrix |
| title_short | Target Detection Using Nonsingular Approximations for a Singular Covariance Matrix |
| title_sort | target detection using nonsingular approximations for a singular covariance matrix |
| url | http://dx.doi.org/10.1155/2012/628479 |
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