基於最差狀況體積最大化之強健端元抽取快速演算法

高光譜分解(hyperspectral unmixing)是指從高光譜數據(hyperspectral data)中抽取出不同物質之光譜特徵(即端元(endmember))與其相應豐度圖(abundance maps)的過程，豐度圖顯示出每個端元在一表面上的含量比例分佈圖。在本論文中，我們著重在如何從受雜訊(noise)影響的數據中，準確地估測出不同物質之光譜特徵。現存的高光譜分解演算法中的其中一個類別是以Winter所提出的端元抽取想法為基礎，其想法為「在純像素(一個像素中僅含有一種物質的光譜特徵)存在的情況下，端元可藉由從量測到的數據雲(data cloud)內找到最大體積單純型(simplex)的頂點決定。」不過，實際上因為數據中存在雜訊的關係，依照Winter的想法所估測出端元之光譜特徵和真正端元之光譜特徵會有相當的誤差。為此，根據強健的Winter的想法和其公式化後的表示式，我們提出兩個演算法，分別稱為最差狀況強健交替式體積最大化(worst-case robust alternating volume maximization, WCR-AVMAX)和最差狀況強健連續式體積最大化(worst-case robust successive volume maximization, WCR-SVMAX)，其中前者是利用了交替式最佳化(alternating optimization)而後者則是連續式最佳化(successive optimization)。前者需要給定初始值但後者不需要且兩者在計算上都有十分有效率。最後，我們利用電腦模擬和真實高光譜實驗(1997年內華達州Cuprite礦區所採集的高光譜數據)並與現存以純像素為基礎的演算法作比較，驗證了我們提出的演算法的優良效能和實用性。

關鍵字

高光譜分解；交替式最佳化；連續式最佳化；端元

並列摘要

Hyperspectral unmixing is a process of extracting the spectral signatures (endmember signatures) and the corresponding fractions (abundance maps), which represent the proportional contribution of each endmember over the surface, from the given hyperspectral data. In this thesis, we focus on the study of how to accurately estimate the endmember signatures in the presence of noise in the observed data. A branch of existing hyperspectral unmixing algorithms is based on Winter's endmember extraction belief, which indicates that in the presence of pure pixels (the pixels are contributed by a single endmember only), the endmembers can be determined by finding the vertices of the maximum-volume simplex inside the data cloud. Nevertheless, in practice the endmember estimates yielded by Winter's belief are not in the proximity of true endmember signatures due to inevitable noise present in the data. Based on the robust Winter's belief and formulation cite{Chan2011}, we propose two algorithms, namely worst-case robust alternating volume maximization (WCR-AVMAX) and worst-case robust successive volume maximization (WCR-SVMAX) which respectively apply alternating optimization and successive optimization to fulfill the robust Winter's belief. The former needs initialization while the later does not, and both are computationally efficient. Finally, we present computer simulations and real data experiments (AVIRIS hyperspectral data taken over the Cuprite mining site, Nevada, 1997 cite{AVIRIS}) to demonstrate the superior performance and practical applicability of our proposed algorithms compared to several benchmark existing pure-pixel based algorithms.

並列關鍵字

hyperspectral unmixing ； alternating optimization ； successive optimization ； endmember

參考文獻

framework for hyperspectral endmember extraction,” to appear in IEEE

Trans. Geoscience and Remote Sensing - Special Issue on Spectral Unmixing of Re-

minimum volume enclosing simplex algorithm for hyperspectral unmixing,” to appear

in IEEE Trans. Geoscience and Remote Sensing - Special Issue on Spectral Unmixing

of Remotely Sensed Data, 2011.

國際替代計量

基於最差狀況體積最大化之強健端元抽取快速演算法

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