高光譜影像解混(hyperspectral unmixing)作為一種有效的技術，用於從給定的高光譜數據(hyperspectral data)中識別端元(endmember，即物質之光譜特徵)及其相對豐度值(abundance fractions)。傳統的線性混合模型(linear mixing model)通常被使用，由於其簡單性; 然而，它隱含地假設單一光譜可以完全代表單一物質。近年來，在高光譜影像解混針對給定的高光譜數據受到不可忽視的端元變異性(endmember variability)或奇異點效應(outlier effect)的影響，引起了人們很大的關注。許多先進的研究試圖在演算法中考慮端元變異性或奇異點效應來提高準確性，但迄今為止沒有一項研究將端元變異性和奇異點效應同時考慮。在本論文中，我們的目的是提出一種簡單彈性的算法，使用殘餘擾動線性混合模型(residual perturbed linear mixing model, rPLMM)分解高光譜圖像。該模型升級了傳統的線性混合模型，它允許端元光譜在每個像素改變，並同時引入額外的正規化項來考慮奇異點效應。我們為病態的逆向問題(ill-posed inverse problem)加入三個合適的正規化項，這也是一個非凸的最小化問題。之後，我們將這個最小化問題重新推演成一個可以透過塊座標下降法(block coordinate descent)解的多凸(multi-convex)問題，並以新的高光譜影像分解演算法(稱為rPLMM 算法)加以實現。最後，我們提供了一些電腦模擬和真實數據實驗結果，證明所提出的rPLMM 演算法之優良效能和適用性，最後對我們的演算法得出一些結論。

Hyperspectral unmixing (HU) works as an effective technique to identify the endmember signatures and their relative abundance fractions from a given hyperspectral data. The conventional linear mixing model (LMM) [1] is often used due to its simplicity; however, it implicitly assumes that a single spectrum can fully represent a material. Recently, the HU study for the given hyperspectral data subject to non-negligible endmember variability (EV) or outlier effects (OE) has drawn significant attention. Quite a few state-of-the-art research papers have attempted to enhance the accuracy of their proposed algorithms by taking the phenomenon of either EV or OE into account, but none has so far considered investigating EV and OE together. In this thesis, we aim to propose a simple and flexible algorithm to unmix hyperspectral image using a residual perturbed linear mixing model (rPLMM). This model upgrades the conventional LMM, which allows a pixel-wise variation of the endmember spectral signature, and introduces an additional regularization term to account for OE in the meantime. We add three suitable regularizers to the ill-posed inverse problem, which is also a nonconvex minimization problem. Then we reformulate the minimization problem into a multi-convex one that can be solved by the block coordinate descent (BCD) method, and implemented by a new HU algorithm, referred to as the rPLMM algorithm. Finally, we provide some simulation results, as well as some real experimental results, to demonstrate the efficacy and practical applicability of the proposed rPLMM algorithm followed by some conclusions.

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