Hyperspectral Data Processing: Algorithm Design and Analysis

12.4 OSP Implemented with Partial Knowledge

In Sections 12.2 and 12.3, OSP assumes the complete knowledge of target signatures, . In many practical applications, obtaining such full knowledge is generally very difficult if not impossible, specifically, when the image background is not known. In this section, we investigate an issue of how to implement OSP when there is no full knowledge available, particularly, for the case that we are only interested in specific targets, but not image background or other natural signatures.

In his dissertation (Harsanyi, 1993), Harsanyi relaxed the requirement of complete knowledge for OSP by developing an approach called CEM to circumvent this dilemma. The idea is to constrain the desired target signature, d with a specific gain while minimizing interfering effects caused by unknown signal sources. Since the undesired target signatures in U used by OSP are assumed to be unknown, the undesired target signatures in U are suppressed by minimizing their energies instead of being annihilated by a specific operator such as used in OSP. Despite the fact that the relationship between OSP and CEM was reported in Chang 2003a, 2003b) and Du et al. (2003), this section takes an alternative approach to show that with the same assumptions made for OSP, CEM actually ...