Convex analysis based minimum-volume enclosing simplex algorithm for hyperspectral unmixing
Convex analysis based minimum-volume enclosing simplex algorithm for hyperspectral unmixing
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DOI：
10.1109/icassp.2009.4959777
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发表时间：
2009-04
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影响因子：
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通讯作者：
Tsung-Han Chan;Chong-Yung Chi;Yu-Min Huang;Wing-Kin Ma
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文献类型：
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作者：
Tsung-Han Chan;Chong-Yung Chi;Yu-Min Huang;Wing-Kin Ma
高光谱解混的目的是从观测到的高光谱场景中识别隐藏的光谱特征（或端元）及其相应的比例（或丰度）。许多现有的高光谱解混方法依赖于纯像素的假设，这可能会违反高度混合的数据。克雷格提出了一种不需要纯像素假设的启发式解混准则：端元估计由包含所有观察像素的最小体积单纯形的顶点确定。在本文中，我们使用凸分析，证明了高光谱解混克雷格的标准可以制定为一个优化问题，找到一个最小体积封闭单纯形（MVES）。还提出了一种通过线性规划（LP）循环求解MVES问题的算法。一些Monte Carlo仿真证明了所提出的MVES算法的有效性。
Hyperspectral unmixing aims at identifying the hidden spectral signatures (or endmembers) and their corresponding proportions (or abundances) from an observed hyperspectral scene. Many existing approaches to hyperspectral unmixing rely on the pure-pixel assumption, which may be violated for highly mixed data. A heuristic unmixing criterion without requiring the pure-pixel assumption has been reported by Craig: The endmember estimates are determined by the vertices of a minimum-volume simplex enclosing all the observed pixels. In this paper, using convex analysis, we show that the hyperspectral unmixing by Craig's criterion can be formulated as an optimization problem of finding a minimum-volume enclosing simplex (MVES). An algorithm that cyclically solves the MVES problem via linear programs (LPs) is also proposed. Some Monte Carlo simulations are provided to demonstrate the efficacy of the proposed MVES algorithm.