Hyperspectral Band Selection by Virtual Dimensionality

Abstract

Hyperspectral images are generally acquired by hundreds of contiguous spectral bands and provide a wealth of useful and crucial information for data analysis. However, on many occasions too many bands cause undesired effects, called curse of dimensionality. Therefore, band selection is generally preferred prior to application in hyperspectral data exploitation. In this dissertations, an information theoretical approach using channel capacity for band subset selection, called channel capacity band subset selection (CCBSS), is proposed. It first constructs a channel with the full band set as channel input space, a selected band subset as channel output space, and band discrimination between the full band set and the selected band subset as channel transition probabilities. Then, Blahut's algorithm is utilized to find the maximal channel capacity by iterating through different selected band subsets as channel output space. As a result, there is no need of band prioritization and inter-band decorrelation generally required by traditional band selection (BS). Two iterative algorithms are developed for finding an optimal BSS, sequential channel capacity BSS (SQ-CCBSS) and successive channel capacity BSS (SC-CCBSS), both of which avoid an exhaustive search for all possible band subset combinations. To justify the utility of CCBSS an application of linear spectral unmixing is used for illustration. Experimental results demonstrate that CCBSS outperforms other traditional band selection approaches in the sense that the targets found using the selected bands have smaller unmixing error. Furthermore, based on the channel model proposed, an objective criterion is designed to measure the capacity of the whole hyperspectral image or selected bands solely based on spectral inter-band discrimination provided by data, not on any particular applications. Its idea is to first construct a band channel for a given hyperspectral data with the channel input space specified by the complete spectral bands, channel output space made up of the bands selected by a particular BS method, and channel transition probabilities calculated by a spectral discrimination measure between a channel input band and a selected band as a channel output band. Then the capacity of the constructed band channel found for this BS method will be used to evaluate its effectiveness for performance analysis. The larger the band capacity is, the better the BS method is. Experiments show that a BS method which yields large BC generally also performs well for most applications. Last but not least, a new Neyman-Pearson-based detection approach, called band-specified virtual dimensionality (BSVD), is proposed to decide how many bands to select, which is an unsolved issue in CCBSS. Its idea is derived from target specified virtual dimensionality (TSVD) where targets are replaced with bands as signal sources. The criterion used to derive bands as signal sources is orthogonal subspace projection (OSP), which is based on maximal signal-to-noise ratio, and the resulting VD is referred to as OSP-BSVD. Several benefits can be offered by BSVD that traditional BS methods cannot. One is its direct approach to dealing with the number of bands to select. 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 the number of bands to select and finds desired bands simultaneously and progressively.