Fast algorithms to implement N-FINDR for hyperspectral endmember extraction

Abstract

N-FINDR suffers from several issues in its practical implementation. One is the search region which is usually the entire data space. Another related issue is its excessive computation. A third issue is the use of random initial conditions which causes inconsistency in final results that can not be reproducible. This paper develops two ways to speed up the N-FINDR in computation. One is to narrow down the search region for the N-FINDR to a feasible range, called region of interest (ROI) where data sphering/thresholding and the well-known pixel purity index (PPI) are used as a preprocessing to find a desire ROI. The other is to simplify the simplex volume computation where three methods are proposed for this purpose to reduce computational complexity of matrix determinant. In addition, in order to further reduce computational complexity two sequential N-FINDR algorithms are developed which implement the N-FINDR by finding one endmember after another in sequence so that the information provided by previously found endmembers can be used to reduce computational complexity. The conducted experiments demonstrate that while the proposed fast algorithms can greatly reduce computational complexity, their performance remains as good as the N-FINDR is and is not compromised by reduction of the search region to an ROI and simplified matrix determinant.