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

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.