在超光譜遙感中，分解一個數據立方體(data cube)成為不同物質的頻譜特徵(端元(endmembers))和其相對應的豐度分數(abundance fractions),在分析固體表面礦物成分，扮演著非常重要的角色。一個純像素是指一個像素是完全的由一個物質的端元所構成，而大部分現存的高光譜分解方法是基於純像素假設的線性混和模型。本論文主要分兩大部分，首先，我們提出了一個估測端元的方法，適用於純像素條件成立的情形，稱之為P 次範數之最純像素鑑別(P-norm based
purest pixel identification (Tri-P))。此演算法是基於P 次範數以及正交投影的觀念。而後，根據已估測到的端元，我們可以使用倒置程序(inversion process)去找到相對應的豐度分數。然而，現存所有的超光譜分解的方法，包括我們所提出的Tri-P，需已知端元的個數為前提。因此，本篇論文的第二部分，提出一個估測端元個數的方法，稱之為基於重生性(reproducibility)模型階數之選擇(reproducibility based model order selection (RMOS))。此演算法是基於Tri-P 演算法以及重生性的概念，以估測端元個數。此外，在模型階數選擇中，我們知道一個好的方法去衡量重生性是非常重要。為了去更可靠地度量重生性，我們提出了一個結合Neyman-Pearson 假設檢定(Hypothesis testing)方法以量化重生性。最後，我們進行 Monte Carlo 模擬以及真實超光譜影像實驗，並和其它基於純像素假設的方法做比較，以展示所提出Tri-P 演算法有較低的運
算複雜度，以及RMOS 有較佳模型階數選擇的效能。

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