Accounting for spectral variability in hyperspectral unmixing using beta endmember distributions
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Hyperspectral imaging is widely used in the field of remote sensing (Goetz, et al., 1985; Green, et al., 1998). In a hyperspectral imaging system, sensors collect radiance/reflectance values over an area (or a scene) across hundreds of spectral bands (Goetz, et al., 1985). The hyperspectral image yielded by such system can be represented by a three-dimensional data cube containing those radiance/reflectance values in a range of wavelengths (Landgrebe, 2002). There are two common analysis methods for hyperspectral imagery (Hu, et al., 1999): endmember estimation and hyperspectral unmixing. Endmember estimation aims at finding pure individual spectral signatures of the materials (endmembers) in the scene (Adams, et al., 1986). Hyperspectral unmixing, on the other hand, estimates the proportions of each endmember at every pixel of the image. Each pixel in the image can then be represented by endmember spectra weighted by its corresponding proportions. In order to increase the accuracy of hyperspectral unmixing, sufficient temporal and spatial spectral variability of endmembers must be taken into consideration (Roberts, et al., 1992; Roberts, et al., 1998; Bateson, et al., 2000). The most common factors contributing to spectral variability include environmental factors, such as atmospheric effects, illumination, moisture conditions, and inherent spectral variability of the material itself, such as the variations in biophysical and biochemical composition in vegetation (Song, 2005). Under such influence, the spectral signature of endmembers may vary from time to time and from pixel to pixel in the scene. In order to account for such endmember spectral variability, endmembers are regarded as either a set, or a "bundle", of individual spectra (Roberts, et al., 1998; Bateson, et al., 2000), or as a sample from a full distribution. The application of the Normal Compositional Model with Gaussian-distributed endmembers has been discussed in the literature (Eches, et al., 2010; Zare, et al., 2012). Since the domain of Gauss
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M.S.