Comparative Study and Analysis Among ATGP, VCA, and SGA for Finding Endmembers in Hyperspectral Imagery

Abstract

Endmember finding has become increasingly important in hyperspectral data exploitation because endmembers can be used to specify unknown particular spectral classes. Pixel purity index (PPI) and N-finder algorithm (N-FINDR) are probably the two most widely used techniques for this purpose where many currently available endmember finding algorithms are indeed derived from these two algorithms and can be considered as their variants. Among them are three well-known algorithms derived from imposing different abundance constraints, that is, abundance-unconstrained automatic target generation process (ATGP), abundance nonnegativity constrained vertex component analysis (VCA), and fully abundance constrained simplex growing algorithm (SGA). This paper explores relationships among these three algorithms and further shows that theoretically they are essentially the same algorithms in the sense of design rationale. The reason that these three algorithms perform differently is not because they are different algorithms, but rather because they use different preprocessing steps, such as initial conditions and dimensionality reduction transforms.