高光譜影像分解(hyperspectral unmixing)是指從高光譜數據(hyperspectral data)中
抽取出不同物質的光譜特徵(即端元(endmember))與端元對應於地表上所含的比
例豐度圖(abundance maps)。維度降低在高光譜影像分解中是常見且首要的過程，
可降低雜訊的影響和降低運算複雜度。仿射集合配適法(affine set fitting)在端元抽
取(endmember extraction)演算法中是非常常見的降維度方法，可以使得高光譜數據
於低維度空間中有最小的平方誤差(least-squares)，然而奇異點(outlier)出現於高光
譜影像中是不可避免的，奇異點會嚴重的影響仿射集合配適法的效能。在本論文
中，我們提出了強健仿射集合配適法(robust affine set fitting)， 希望同時達到偵測
奇異點與提供強健仿射集合的目標。假定我們已知高光譜影像中的端元數和影像
中的奇異點個數，不同於傳統的奇異點偵測演算法需要窗戶(window)的設置，強
健仿射集合配適法是藉由估測無雜訊和奇異點影響的數據(noise-outlier-free data)
和有奇異點存在的數據(outlier-data)使此兩項數據值有最小平方誤差。接著我們提
出了RASF-NP 演算法，結合了RASF 和Neyman-Pearson 假設檢定(hypothesis testing)
我們可以進一步的估測出準確的奇異點個數。經過RASF-NP 除去奇異點之後，
高光譜影像分解將可以達到更好的效能。最後我們利用電腦模擬和真實影像實驗
(內華達州LCVF 地區採集之高光譜影像)和現存的奇異點偵測演算法做比較，驗
證了我們提出的演算法之優良效能和優良的運算效率。

Hyperspectral umnixing is a process to extract the spectral signatures (endmembers) and
the corresponding fractions (abundance maps) from the observed hyperspectral data of
an area. Dimension reduction is a common, primary step in hypserspectral unmixing
with the benefit of reducing noise effect and computation complexity. The affine set
fitting [1] which provides the best representation to a given noisy hyperspectral data in the
least-squares error sense is used as the dimension reduction method in many endmember
extraction algorithms; however, the presence of outliers in the data has been proved to
severely degrade the accuracy of affine set fitting. In this thesis, unlike conventional
outlier detectors which may be sensitive to window settings, we propose a robust affine
set fitting (RASF) algorithm for joint dimension reduction and outlier detection without
any window setting. Given the number of outliers and endmembers in advance, the RASF
algorithm is to find a data-representative affine set from the noise-outlier corrupted data,
while making the effects of outliers minimum, in the least-squares error sense. The
proposed RASF algorithm is then combined with Neyman-Pearson hypothesis testing,
termed RASF-NP, to further estimate the number of outliers present in the data. By
using RASF-NP, we can discard the outlier pixels and find a robust affine set to improve
the consequent hyperspectral unmixing processing. Finally, we present simulations and
real data experiment (AVIRIS hyperspectral data taken from LCVF site, Nevada [2])
to demonstrate the superior performance and computation efficiency of our proposed
algorithm to some existing outlier detection algorithms.

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