Reducing the Complexity of the N-FINDR Algorithm for Hyperspectral Image Analysis

Abstract

The N-FINDR algorithm for unmixing hyperspectral data is both popular and successful. However, opportunities for improving the algorithm exist, particularly to reduce its computational expense. Two approaches to achieve this are examined. First, the redundancy inherent in the determinant calculations at the heart of N-FINDR is reduced using an LDU decomposition to form two new algorithms, one based on the original N-FINDR algorithm and one based on the closely related Sequential N-FINDR algorithm. The second approach lowers complexity by reducing the repetition of the volume calculations by removing pixels unlikely to represent pure materials. This is accomplished at no additional cost through the reuse of the volume calculations inherent in the Sequential N-FINDR algorithm. Various thresholding methods for excluding pixels are considered. The impact of these modifications on complexity and the accuracy is examined on simulated and real data showing that the LDU-based approaches save considerable complexity, while pixel reduction methods, with appropriate threshold selection, can produce a favorable complexity-accuracy trade-off.

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

“…Therefore, the average outer loop numbers of N-FINDR1 (N-FINDR2), LDU-N-FINDR (LDU-S-N-FINDR), and MN-FINDR1 (LDU-S-N-FINDR) are the same. Details on the equivalence between N-FINDR1 (N-FINDR2) and LDU-N-FINDR (LDU-S-N-FINDR) can be found in Dowler, Takashima, and Andrews (2013).…”

“…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).…”

“…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).…”

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].…”