Hyperspectral endmember extraction using convexity based purity index

The endmember extraction is a challenging problem in spectral unmixing (SU) of a mixed pixel in hyperspectral imagery. There are plenty of attempts to solve the endmember extraction problem. Still, the pure pixel assumption-based algorithms have probably been used most in solving the endmember extraction of SU due to the light computational burden. These pure pixel assumption-based algorithms usually follow one of the criteria: (1) Maximum simplex volume or (2) Extreme projection on a subspace. We propose a novel integrated framework that uses both the criteria mentioned above and the proposed one is referred to as the Convexity-based Pure Index (CPI) algorithm. The CPI generates a fixed number of convex sets based on the number of available bands in the hyperspectral image. The algorithm defines the purity score based on the availability of pixels in the convex sets for the two-band data. The CPI has been compared with contemporary algorithms such as Automatic Target Generation Process (ATGP), Vertex Component Analysis (VCA), Pixel Purity Index (PPI), Successive Volume MAXimization (SVMAX), Alternating Volume MAXimization (AVMAX), TRIple-P: P-norm based Pure Pixel identification (TRIP), Successive Decoupled Volume Max–Min (SDVMM), Negative ABundance-Oriented (NABO), and Entropy-based Convex Set Optimization (ECSO). The metrics, Spectral Angle Distance (SAD) and Spectral Information Divergence (SID) used in the comparison were improved up to 5.9 % and 9 % , respectively. The CPI outperforms prevailing algorithms on real benchmark data and new AVIRIS-NG data. The robustness of the CPI is also tested for various noisy synthetic data. The efficacy of the proposed algorithm is also tested by using qualitative analysis by visualizing the spectra comparison, and abundance maps for all real data.