Hyperspectral Data Processing: Algorithm Design and Analysis

27.2 Orthogonal Subspace Projection-Based Band Prioritization Criterion

Orthogonal subspace projector (OSP) approach has been widely used for hyperspectral target detection and classification (Harsanyi and Chang, 1994). It extends a standard signal detection model by dividing signature vectors of interest into two types of signals, called desired target signature vector, d, to be detected and undesired target signature vectors to be eliminated. The performance in detecting d can be improved by eliminating the undesired signature vectors prior to detection of d. This section extends the OSP concept to a band prioritization criterion.

Assume that U is an undesired signature matrix formed by placing all undesired target signature vectors as its column vectors. To eliminate all the signature vectors in U, an orthogonal subspace projector specified by (2.86) can be used for this purpose and defined by

(27.1)

where is the pseudoinverse of U and I is an identity matrix. Applying to a hyperspectral signature vector s leads to a new signature vector denoted by defined as follows:

(27.2)