Hyperspectral image nonlinear unmixing and reconstruction by ELM regression ensemble

Unmixing is the estimation of hyperspectral image pixels composition, specified as the fractional abundances of the composing materials, achieving image segmentation at sub-pixel resolution. Linear unmixing assumes that pixels are convex combinations of endmember spectra, hence endmember identification is required prior to unmixing processes. In our approach to non-linear unmixing by Extreme Learning Machine (ELM) regression ensembles, we do not need to perform endmember identification, which is implicit in the non-linear transformation. Instead we provide estimates of the fractional abundances of predefined material classes, which have been characterized by pure pixels extracted from the image according to available ground truth. In this paper, we introduce a formal discussion of the convergence properties of ELM regression ensembles that endorses the empirical results. The analysis shows them to converge to the exact regression value when the number of components of the ensemble grows, provided that the output is the average of the individual outputs. Besides, the proposed approach allows for a general validation procedure based on the reconstruction error over the entire hyperspectral image. Reconstruction error can be estimated using the mapping from fractional abundances to reconstructed spectra, also achieved by ELM regression ensembles. Therefore, validation can be carried out independently of training data, which can be used completely for model construction. Experimental results on well known benchmark images show that the approach has big advantage over state-of-the-art unmixing approaches.