Hyperspectral Band Selection via Joint Volume Gradient

Unsupervised band selection (BS) is a crucial research direction in the domain of hyperspectral image (HSI) processing. In recent years, volume-based criteria have garnered considerable attention, with the volume-gradient-based BS (VGBS) algorithm being particularly notable. However, we have identified that VGBS inherently suffers from the local extremum problem due to its reliance on the original volume gradient formula, which only permits the removal of a single band per iteration. To address this issue, we introduce the concept of joint volume gradient (JVG) through a novel determinant formula for the high-order mixed product expansion. We then propose an enhanced version of VGBS, termed JVG-based BS (JVGBS), which allows for the simultaneous deletion of multiple bands. Moreover, a simplified objective function of JVG is developed to mitigate the high computational complexity associated with calculating volume metrics when a small number of bands is removed at once. Regarding the complexity imposed by the large cardinality of traversing matrix column combinations, we provide an exemplary algorithm employing groupwise strategies to achieve rapid computational acceleration. Experimental results on Gaofen-5 and publicly available hyperspectral datasets demonstrate that the proposed algorithms have rather superior performance against state-of-the-art competitors in terms of both computational complexity and classification accuracy.