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, i.e. 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 article 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.