Band-Specified Virtual Dimensionality for Band Selection: An Orthogonal Subspace Projection Approach

This paper develops a new Neyman–Pearson detection approach, to be called band-specified virtual dimensionality (BSVD), to estimating the number of bands required by band selection (BS),
$n_{\mathrm {BS}}$
, as well as finding desired bands at the same time. Its idea is derived from target-specified virtual dimensionality (TSVD) where targets under hypotheses as signal sources in TSVD are replaced with bands as signal sources and the test statistics derived for a Neyman–Pearson detector (NPD) is signal-to-noise ratio (SNR) that is used to derive orthogonal subspace projection (OSP) approach for hyperspectral image classification and dimensionality reduction. Accordingly, the resulting virtual dimensionality is referred to as OSP-based BSVD. Several benefits resulting from BSVD cannot be offered by the traditional BS methods. One is its direct approach to dealing with
$n_{\mathrm {BS}}$
. Another is no-search strategy needed for finding optimal bands. Instead, it uses NPD to determine and rank desired bands for band prioritization. Most importantly, it determines
$n_{\mathrm {BS}}$
and finds desired bands simultaneously and progressively.