Bootstrapping for Piece-Wise Convex Endmember Distribution Detection

A hyperspectral endmember detection and spectral unmixing algorithm that finds multiple sets of endmember distributions is presented. If endmembers are represented as random vectors, then they can be characterized by a multivariate probability distribution. These distributions are referred to as endmember distributions. The proposed method combines the Piece-wise Convex Multiple Model Endmember Detection (PCOMMEND) algorithm, the Sparsity Promoting Iterated Constrained Endmembers (SPICE) algorithm, and the Competitive Agglomeration (CA) algorithm to estimate endmember distributions. The goal is to produce distributions that are suitable for inclusion into the Normal Compositional Model (NCM). PCOMMEND forms a fuzzy partition of the spectral pixels into a collection of fuzzy convex sets. Each convex set is defined by a set of endmembers and the linear mixing model. In this way, non-convex hyperspectral data are more, accurately characterized. The SPICE algorithm estimates the number of endmembers, the endmembers, and the abundances for each convex set. This process is repeated several times; each time a set of endmembers is produced. The collection of all such sets is merged into a single set of endmembers. This set is clustered using the CA algorithm, which estimates the number of endmembers by estimating the number of clusters and prototypes for each cluster in the single set of endmembers. These prototypes are taken to be the means of endmember distributions. The covariances are estimated by assigning each endmember to the closest prototype and estimating the covariance of that set. The resulting distributions are suitable for the NCM model. Results are shown for the PAVIA data set.