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Automatic discovery and curve fitting of absorption bands in hyperspectral data can enable the analyst to identify materials present in a scene by comparison with library spectra. This procedure is common in laboratory spectra, but is challenging for sparse hyperspectral data. A procedure for robust discovery of overlapping bands in hyperspectral data is described in this paper. The method is capable of automatically discovering and fitting symmetric absorption bands, can separate overlapping absorption bands in a stable manner, and has relatively low sensitivity to noise. A comparison with techniques already available in the literature is presented using simulated spectra. An application is demonstrated utilizing the shortwave infrared (2.0-2.5 μm or 5000-4000 cm-1) region. A small hyperspectral scene is processed to demonstrate the ability of the method to detect small shifts in absorption wavelength caused by varying white mica chemistry in a natural setting.