Hyperspectral Data Processing: Algorithm Design and Analysis

12.5 OSP Implemented Without Knowledge

As OSP was originally developed in Harsanyi and Chang (1994), it required complete endmember knowledge about the image data. Unfortunately, such requirement is seldom satisfied in reality. In order to resolve this issue, two approaches are developed previously. One is to generate desired complete knowledge directly from the image data in an unsupervised means so that the obtained unsupervised knowledge can be used as if it was provided a priori (Chang, 2003a, Chang et al., 2001) to make (d,U)-model applicable where the undesired target signature projector can be constructed from the generated U. Due to the fact that such generated unsupervised knowledge may not be accurate or reliable, an alternative approach is to implement OSP without appealing for unsupervised knowledge. One such approach is CEM described in Section 12.4.1 where only the desired target knowledge, d, is required. Instead of trying to find unknown signatures in U for annihilation, CEM suppresses all signatures other than the signature of interest. To accomplish that, CEM makes use of the inverse of the sample correlation matrix, to approximate the complete knowledge provided by in OSP. As a result, OSP and CEM can be related by (12.72)–(12.74) using TCIMF to bridge the gap. ...