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22 May 2014 A theory of least-squares target-specified virtual dimensionality in hyperspectral imagery
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Virtual dimensionality (VD) has received considerable interest in its use of specifying the number of spectrally distinct signatures, denoted by p. So far all techniques are eigen-based approaches which use eigenvalues or eigenvectors to estimate the value of p. However, when eigenvalues are used to estimate VD such as Harsanyi-Farrand-Chang’s method or hyperspectral signal subspace identification by minimum error (HySime), there will be no way to find what the spectrally distinct signatures are. On the other hand, if eigenvectors/singular vectors are used to estimate VD such as maximal orthogonal complement algorithm (MOCA), eigenvectors/singular vectors do not represent real signal sources. Most importantly, current available methods used to estimate VD run into two major issues. One is the value of VD being fixed at a constant. The other is a lack of providing a means of finding signal sources of interest. As a matter of fact, the spectrally distinct signatures defined by VD should adapt its value to various target signal sources of interest. For example, the number of endmembers should be different from the number of anomalies. In this paper we develop a second-order statistics approach to determining the value of the VD and the virtual endmember basis.
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Drew Paylor and Chein-I Chang "A theory of least-squares target-specified virtual dimensionality in hyperspectral imagery", Proc. SPIE 9124, Satellite Data Compression, Communications, and Processing X, 912402 (22 May 2014);

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