National Geospatial-Intelligence Agency, Springfield, VA 22150, USA.
IEEE Trans Image Process. 2012 Jan;21(1):219-28. doi: 10.1109/TIP.2011.2160189. Epub 2011 Jun 20.
In the LMM for hyperspectral images, all the image spectra lie on a high-dimensional simplex with corners called endmembers. Given a set of endmembers, the standard calculation of fractional abundances with constrained least squares typically identifies the spectra as combinations of most, if not all, endmembers. We assume instead that pixels are combinations of only a few endmembers, yielding abundance vectors that are sparse. We introduce sparse demixing (SD), which is a method that is similar to orthogonal matching pursuit, for calculating these sparse abundances. We demonstrate that SD outperforms an existing L(1) demixing algorithm, which we prove to depend adversely on the angles between endmembers. We combine SD with dictionary learning methods to calculate automatically endmembers for a provided set of spectra. Applying it to an airborne visible/infrared imaging spectrometer image of Cuprite, NV, yields endmembers that compare favorably with signatures from the USGS spectral library.
在高光谱图像的 LMM 中，所有图像光谱都位于一个具有称为端元的角的高维单形上。给定一组端元，用约束最小二乘法进行分数丰度的标准计算通常会将光谱识别为大多数（如果不是全部）端元的组合。相反，我们假设像素是少数几个端元的组合，产生稀疏的丰度向量。我们引入稀疏解混（SD），这是一种类似于正交匹配追踪的方法，用于计算这些稀疏丰度。我们证明了 SD 优于现有的 L(1)解混算法，该算法被证明与端元之间的角度不利相关。我们将 SD 与字典学习方法结合起来，为提供的一组光谱自动计算端元。将其应用于内华达州 Cuprite 的机载可见/红外成像光谱仪图像，得到的端元与 USGS 光谱库中的特征值相比具有优势。
