臺灣博碩士論文加值系統

由於影像空間解析度之限制，遙測影像中之單一像素通常包含兩種以上的成份物質。解析混合光譜 (spectral unmixing) 技巧主要被使用在決定單一像素中不同成分物質，又稱端元 (endmember)，及各個成份物質在單一像素中所佔的豐度 (abundance)。假設影像中存在由單一成分物質所構成的像素來表示我們有興趣的端元。換句話說，端元即是在給定的維度下包含所有資料點之幾何形狀的端點。則大部分解析混合技巧可直接由影像中導出端元。不過在許多情況下這個假設是不成立的。在這邊，我們主要研究當影像中不存在純像素時，解析混合光譜所遭遇到的問題。
K-L距離可用來測量觀測豐度分配與假設的豐度分配間的差異度。我們將解析混合光譜問題看成是一個受限制的最小化問題，使K-L距離最小化且豐度滿足和為一及非負的限制。在豐度分配資訊已知時，最小化K-L距離可以獲得最佳的端元。在遺失端元的問題中，最小化K-L距離相當於限制資料點在樣本空間上的幾何形狀，使得端元即是受限制的幾何形狀之端點。
我們將提出的方法和一些光譜解混技術，如頂點成分分析法 (vertex component analysis)、非監督式完全限制最小平方法 (unsupervised fully constrained least squares linear unmixing)、獨立成份分析法 (ndependent component analysis)、和疊代限制端元法 (iterated constrained endmembers)進行比較。經由特別設計的模擬資料和真實影像資料來評估提出的方法的效能。在缺乏端元的情況中，這些端元萃取的方法並無法得到正確的結果，相對的提出的方法可得到可靠的結果。結果顯示限制型K-L距離可以有效的被應用在解析混合光譜上。

Due to limited spatial resolution, a pixel often consists of two or more substances in remote sensing imagery. Spectral unmixing techniques have been intensively used for determining the abundance of a substance, also referred to as an endmember, in a pixel. Most unmixing methods that derive endmembers directly from an image assume that there exist pure pixels in the image corresponding to the endmembers of interest. That is, the endmembers are the vertices of a simplest geometric shape that can enclose a space of a given dimension. However, this assumption may not hold in many cases. In this study, we investigated the spectral unmixing problems where the pure pixels may not be present in the image.
The Kullback-Leibler (K-L) distance has been used as a measure for the dissimilarity between the observed distribution and a hypothetic distribution. We formulated the spectral unmixing problem as a constrained minimization problem of the K-L distance subject to the sum-to-one and the nonnegativity constraints on abundances. For the missing endmember problem, minimizing the K-L distance can constrain the geometric shape of the data points in the sample space so that the vertices of a geometric shape will be the endmembers.
We compared the proposed method with several spectral unmixing techniques, such as vertex component analysis (VCA), unsupervised fully constrained least squares linear unmixing (UFCLSLU), independent component analysis (ICA), and iterated constrained endmembers (ICE). The proposed method was evaluated in some spectrally designed frameworks that using both simulated and real data. In case of missing endmembers, the presented method produced relatively reliable results, compared to the other spectral unmixing techniques extracted. This indicates the feasibility of the constrained K-L distance for spectral unmixing applications.

1. Introduction 1
1.1 Motivation 1
1.2 Objective 5
1.3 Organization 5
2. Related Work 7
2.1 Introduction 7
2.2 Linear Mixing Model 7
2.3 Algorithms for Linear Unmixing 8
2.4 Vertex Component Analysis (VCA) 10
2.5 Unsupervised Fully Constrained Least Squares
Linear Unmixing Algorithm (UFCLSLU) 11
2.6 Independent Component Analysis (ICA) 14
2.6.1 Preprocessing for ICA 15
2.6.2 Objective function for ICA 16
2.7 Iterated Constrained Endmembers (ICE) 19
3. The Proposed Method 21
3.1 Introduction 21
3.2 Kullback-Leibler Distance 21
3.3 The Iterated Abundance Distribution Method 22
3.4 The Algorithm of Constrain K-L Distance 25
4. Experimental Results 27
4.1 Introduction 27
4.2 Simulated Data 28
4.2.1 Simulation-I 28
4.2.2 Simulation-II 29
4.2.3 Simulation-III 31
4.2.4 Simulation-IV 34
4.3 Real Data 39
4.3.1 Data descriptions 39
4.3.2 FORMOSAT-2 imagery 43
5. Conclusions 59
References 61

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