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Journal of Electrical and Computer Engineering
Volume 2012 (2012), Article ID 628479, 7 pages
http://dx.doi.org/10.1155/2012/628479
Research Article

Target Detection Using Nonsingular Approximations for a Singular Covariance Matrix

1Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
2Department of Geography and Environmental Development, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
3Signal and Image Centre, Royal Military Academy, 1000 Brussels, Belgium

Received 1 April 2012; Accepted 7 June 2012

Academic Editor: Xiaofei Hu

Copyright © 2012 Nir Gorelik et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.