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Orthogonal Subspace Projection Revisited
The orthogonal subspace projection (OSP) approach has received considerable interests in hyperspectral image classification since it was first developed in 1994 (Harsanyi and Chang, 1994). It has been shown to be a versatile technique for a wide range of applications in subpixel detection (Chang, 2003a), mixed classification (Chang, 2003a), dimensionality reduction in Chapter 6, virtual dimensionality (VD) estimation in Chapter 5, and variable-number variable-band selection (VNVBS) in Chapter 27. Unfortunately, insights into its design rationale have not been explored in the past. In this chapter, we revisit this technique and study OSP from several signal processing perspectives. In particular, we further conduct an in-depth investigation in an issue of how to effectively operate OSP using different levels of a priori target knowledge for target detection and classification. Additionally, we also look into various assumptions made on OSP, which result in filters with different forms, some of which turn out to be well-known and popular target detectors and classifiers. Interestingly, we also show how OSP is related to the commonly used least-squares-based linear spectral mixture analysis (LSMA) and how OSP takes advantage of Gaussian noise to arrive at the Gaussian maximum likelihood detector/estimator and likelihood ratio test. Extensive experiments are also conducted to simulate scenarios to illustrate the utility of OSP operating ...
