A Review of Virtual Dimensionality for Hyperspectral Imagery

Virtual dimensionality (VD) is originally defined as the number of spectrally distinct signatures in hyperspectral data. Unfortunately, there is no provided specific definition of what "spectrally distinct signatures" are. As a result, many techniques developed to estimate VD have produced various values for VD with different interpretations. This paper revisits VD and interprets VD in the context of Neyman-Pearson detection theory where a VD estimation is formulated as a binary composite hypothesis testing problem with targets of interest considered as signal sources under the alternative hypothesis, and the null hypothesis representing the absence of targets. In particular, the signal sources under both hypotheses are specified by three aspects. One is signal sources completely characterized by data statistics via eigenanalysis, which yields Harsanyi-Farrand-Chang method and maximum orthogonal complement algorithm. Another one is signal sources obtained by a linear mixing model fitting error analysis. A third one is signal sources specified by inter-band spectral information statistics which derives a new concept, called target-specified VD. A comparative analysis among these three aspects is also conducted by synthetic and real image experiments.