The Sparse Matrix Transform for Covariance Estimation and Analysis of High Dimensional Signals

2011 ◽  
Vol 20 (3) ◽  
pp. 625-640 ◽  
Author(s):  
Guangzhi Cao ◽  
Leonardo R. Bachega ◽  
Charles A. Bouman
Keyword(s):  
Sparse Matrix ◽  
Covariance Estimation ◽  
High Dimensional ◽  
Sparse Matrix Transform

scholarly journals Target Detection Using Nonsingular Approximations for a Singular Covariance Matrix

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Nir Gorelik ◽  
Dan Blumberg ◽  
Stanley R. Rotman ◽  
Dirk Borghys
Keyword(s):  
Covariance Matrix ◽  
Sparse Matrix ◽  
Difficult Problem ◽  
Covariance Matrix Estimation ◽  
High Dimensional ◽  
Matrix Estimation ◽  
Givens Rotations ◽  
Sparse Matrix Transform ◽  
Singular Covariance Matrix ◽  
Global Covariance

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.

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