12.3 Gaussian Noise in OSP
The noise assumed in (12.1) is nothing more than additive, zero-mean, and white. More precisely, the noise assumed in (12.1) is uncorrelated with target signatures in M and is a zero-mean de-correlated (i.e., the noise covariance matrix is an identity matrix) random process. These two assumptions are not crucial and can be relaxed by data preprocessing. The assumption of additivity can be achieved by an estimation technique such as LS methods (Tu et al., 1997; Chang et al., 1998; Chang, 2003a) to remove correlation between target signal subspace and noise subspace. The assumption of zero-mean white noise can be accomplished by a prewhitening process described in Section 6.3.1, a widely used technique in communications and signal processing community (Poor, 1994). Since SNR is generally very high in hyperspectral imagery, the correlation of the noise subspace with the target signature subspace is significantly reduced compared to that in multispectral imagery. This may be one of the major reasons that OSP has been successful even though it violates the additivity assumption and white noise, but the consequence does not cause much performance deterioration. Nevertheless, by taking advantage of the Gaussian assumption many research efforts have produced satisfactory results (Tu et al., 1997; Chang et al., 1998; Chang, 2003a; Manolakis, 2001) as follows.
12.3.1 Signal Detector in Gaussian Noise Using OSP-Model
In this section, we investigate the role of Gaussian ...