Abundance guided endmember selection: An algorithm for unmixing hyperspectral data

Abstract

Linear unmixing is a blind source separation problem that decomposes a hyperspectral image into the spectra of the material constituents of the scene and the abundance maps of those materials across that scene. A novel method for determining the material spectra from within the scene, AGES, is proposed based on the positional information contained within abundances generated by additivity-constrained inversion. This new approach is compared on both simulated and real data sets to the well established N-FINDR algorithm, comparing favorably in terms of computational complexity with the existing algorithm without significantly sacrificing accuracy. In addition, the algorithm has some desirable properties inherent in such an approach.

A Novel Negative Abundance‐Oriented Hyperspectral Unmixing Algorithm

“…The main differences between the proposed NABO algorithm and the aforementioned abundance-guided methods [30], [31] are the following. • We propose a methodology to introduce the estimation of the number of endmembers as an inherent part of the unmixing process.…”

“…On the other hand, normalizing the abundances introduces another source of error in the process of estimating the number of endmembers since the length of the reconstructed pixels is modified. • We propose the use of a global objective function in NABO to identify the substituted endmember, in contrast with [30] and [31], where no criteria are followed. This global function avoids the selection of outliers as candidate endmembers and offers a more straightforward stopping rule than the a priori selection of a tolerance value.…”

“…Recently, methods based on estimated abundance to guide the endmember induction process have been proposed [30], [31]. These methods assume that the pixels with highest abundance absolute values for some set of candidate endmembers are better candidates to be the actual endmembers.…”

“…This is based on the error between the original image and the reconstructed one using the unconstrained abundances; therefore, the error can only be explained in terms of noise and lack of dimensionality. • The proposed NABO method imposes no constraints to the abundance estimation, and the search is guided by the maximum negativity; whereas, in [30] and [31], sum-toone constraint is imposed and the search is guided by the maximum absolute value. Both criteria are similar since a high absolute value (greater than one) with sum-to-one constraint implies negative abundance of at least one of the components of the abundance vector.…”

“…• In addition, we propose a more conservative methodology to select the new candidate endmember and the old endmember that the new endmember will substitute. In [30] and [31], the pixel with maximum absolute abundance is selected to substitute the endmember corresponding to the index of such abundance. The proposed NABO methodology selects a set of candidate pixels ordered by maximum negative abundance.…”