Fast Algorithms to Implement N-FINDR for Hyperspectral Endmember Extraction

Abstract

The N-finder algorithm (N-FINDR) suffers from several issues in its practical implementation. One is its search region which is usually the entire data space. Another related issue is its excessive computation. A third issue is its use of random initial conditions which causes inconsistency in final results that can not be reproducible if a search for endmembers is not exhaustive. This paper resolves the first two issues by developing two approaches to speed-up of the N-FINDR computation while implementing a recently developed random pixel purity index (RPPI) to alleviate the third issue. First of all, it narrows down the search region for the N-FINDR to a feasible range, called region of interest (ROI), where two ways are proposed, data sphering/thresholding and RPPI, to be used as a pre-processing to find a desired ROI. Second, three methods are developed to reduce computing load of simplex volume computation by simplifying matrix determinant. Third, to further reduce computational complexity three sequential N-FINDR algorithms are implemented by finding one endmember after another in sequence instead of finding all endmembers together at once. 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

Fast implementation of linear and nonlinear simplex growing algorithm for hyperspectral endmember extraction

“…To reduce computational complexity, different modified N-FINDR approaches are developed [15][16][17][18]. As for SGA, different fast volume calculation approaches are also proposed [19][20][21].…”

Modified N-FINDR endmember extraction algorithm for remote-sensing imagery

“…The first is to narrow the search region from the entire region to a feasible region, which presumes to include all potential endmembers, using an endmember initialization algorithm (EIA) (Plaza and Chang 2005;Chowdhury and Alam 2007;Wei et al 2011;Dowler, Takashima, and Andrews 2013). The second is to simplify the computation of the matrix determinant in volume calculation (Xiong et al 2011;Dowler, Takashima, and Andrews 2013). This method takes advantage of only one column needing to be replaced while all others remain unchanged.…”

“…The third is to develop a parallel implementation of the N-FINDR algorithm on commercial graphical processing units (GPUs) (Sanchez, Marti, and Plaza 2010;Wu et al 2013), to take the advantage of the increased processing power of such units. These three methods are not mutually exclusive, and different versions of combinations have been studied to further reduce N-FINDR's computational expense (Xiong et al 2011;Dowler, Takashima, and Andrews 2013).…”

“…This applies the geometrical formulation of the barycentric coordinates (Honeine and Richard 2012) and derives an equivalent algebraic method for Winter's N-FINDR. In previous studies, researchers have tried to develop a less computationally expensive formula for volume (Xiong et al 2011;Dowler, Takashima, and Andrews 2013), but it would not change the iterative characteristics of N-FINDR. Therefore, the new N-FINDR remains a three-loop algorithm and the improvement in computational effectiveness is limited (Xiong et al 2011).…”

“…In previous studies, researchers have tried to develop a less computationally expensive formula for volume (Xiong et al 2011;Dowler, Takashima, and Andrews 2013), but it would not change the iterative characteristics of N-FINDR. Therefore, the new N-FINDR remains a three-loop algorithm and the improvement in computational effectiveness is limited (Xiong et al 2011). However, our algorithm can change volume comparison to a barycentric coordinate comparison or abundance comparison derived from a least-squares method, thereby potentially considerably reducing the computational complexity.…”