Estimation of Effective Spectral Dimensionality for Hyperspectral Imagery

Due to its use of hundreds of contiguous spectral channels, a hyperspectral imaging sensor can now uncover many material substances which cannot be identified by prior knowledge or by visual inspection. Therefore, it is very challenging and difficult to determine how many spectral signal sources are present in a hyperspectral image. The research in this dissertation investigates this problem and is directed toward estimation of effective spectral dimensionality (ESD) of hyperspectral imagery, which can be considered as an extension of virtual dimensionality (VD) recently introduced by Chang and Du in hyperspectral imagery. In doing so, the orthogonal subspace projection (OSP) is first introduced to estimate VD, where the spectrally distinct signatures, called virtual endmembers (VE) can be obtained at the same time during the process. A similar concept to OSP is further explored for VD estimation where the maximum orthogonal complement algorithm (MOCA) is developed. It turns out that the MOCA is a variation of automatic target generation process (ATGP) implemented coupled with Neyman-Pearson detector along with super-Gaussian noise assumption. The high-order statistics is the further studied where the Harsany-Farrand-Chang (HFC) algorithm used to estimate the VD is extended to high-order statistics HFC algorithm where the probability distributions under the Neyman-Pearson test are obtained by MOCA. In order to demonstrate the utility of the ESD, endmember extraction is used as an application for experiments. In order to efficiently implement the N-FINDR several fast algorithms of N-FINDR are developed to reduce computational complexity. These include re-derivations of four sequential versions of N-FINDR and three different effective ways to calculate matrix determinants involved in simplex volume computation. Finally, to conclude this dissertation, an FPGA design of N-FINDR is investigated for potential hardware implementation. Since N-FINDR does not have prior knowledge of the number of endmembers, p required to generate, a direct FPGA implementation of the N-FINDR is unrealistic. In this case, the FPGA implementation for a sequential version of N-FINDR, Simplex Growing Algorithm (SGA) is investigated as an alternative to resolve this issue. It turns out that the FPGA of the SGA can be implemented in such a way that the value of the p can vary with different data sets, a task that cannot be accomplished by any FPGA design of N-FINDR