Hyperspectral Data Processing: Algorithm Design and Analysis

17.2 Least Squares-Based ULSMA

An LS-based approach designs an LS-based algorithm that can be first applied to the original data to extract data sample vectors characterized by second-order statistics of IBSI(S) as BKG signatures and then is applied again to the sphered data to capture data sample vectors characterized by HOS of IBSI(S) as target signatures. The task of data sphering is designed to remove the data sample mean and co-variances while making data variances unity so that data sample vectors completely characterized by second-order statistics of IBSI(S) will be forced on the sphere and all other data sample vectors that are characterized by HOS of IBSI(S) are either inside (sub-Gaussian samples) or outside the sphere (super-Gaussian samples). As a consequence, data sample vectors characterized by IBSI(S) of orders higher than 2 can be extracted from inside or outside the sphere. Interestingly, the idea of using the same algorithm applied to different data sets resulting from the same data set to be processed has never been explored until Chang et al. (2010, 2011).

In what follows, three least squares (LS)-based algorithms developed for SQ-EEAs in Chapter 8 can be used for the purpose of finding VSs directly from the data. The first algorithm is ATGP that is an orthogonal subspace projection (OSP)-based algorithm. Since the OSP is a least squares-based criterion, the ATGP can be also viewed as an unsupervised version of an unconstrained LS-based LSMA method. A second ...