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

The N-FINDR, developed by Winter, is one of the most widely used algorithms for endmember extraction for hyperspectral images. N-FINDR usually needs an outer loop to control the stopping rule and two inner loops for pixel replacement, so it suffers from computational inefficiency, particularly when the size of the remote-sensing image is large. Recently, geometric unmixing using a barycentric coordinate has become a popular research field in hyperspectral remote sensing. According to Cramer's rule, a barycentric coordinate estimated by the ratios of simplex volumes is equivalent to a least-squares solution of a linear mixture model. This property implies a brand new strategy for endmember extraction. In other words, we can deduce endmembers by comparison only of abundances derived from a least-squares approach rather than a complicated volume comparison in N-FINDR. Theoretical analysis shows that the proposed method has the same performance as N-FINDR but with much lower computational complexity. In the experiment using real hyperspectral data, our method outperforms several other N-FINDR-based methods in terms of computing times.