Fast implementation of kernel simplex volume analysis based on modified Cholesky factorization for endmember extraction

Abstract

Endmember extraction is a key step in the hyperspectral image analysis process. The kernel new simplex growing algorithm (KNSGA), recently developed as a nonlinear alternative to the simplex growing algorithm (SGA), has proven a promising endmember extraction technique. However, KNSGA still suffers from two issues limiting its application. First, its random initialization leads to inconsistency in final results; second, excessive computation is caused by the iterations of a simplex volume calculation. To solve the first issue, the spatial pixel purity index (SPPI) method is used in this study to extract the first endmember, eliminating the initialization dependence. A novel approach tackles the second issue by initially using a modified Cholesky factorization to decompose the volume matrix into triangular matrices, in order to avoid directly computing the determinant tautologically in the simplex volume formula. Theoretical analysis and experiments on both simulated and real spectral data demonstrate that the proposed algorithm significantly reduces computational complexity, and runs faster than the original algorithm.