近年來，高頻譜影像已普遍應用於遙測影像之目標物偵測，其優點在於接近連續的數百個頻譜波段可以提供較多高頻譜解析度以解決多頻譜影像無法辨認出之物質。然而在高頻譜影像中感興趣之目標物尺寸一般皆小於地面解析度，在這個情況下，便必須使用次像素目標偵測法。 線性頻譜混合分析是一個常用於高頻譜影像中次像素目標物偵測與物質分類之技術，而最小平方誤差方法則為一個普遍用於解決物質含量估計之線性頻譜混合問題。在本篇論文中將介紹一個一般化之最小平方法，加權最小平方法。當使用不同的加權矩陣時，即可推導出不同的偵測或分類演算法。我們將證明過去一些已發表之方法，皆可重寫為加權最小平方法的形式。為了產生更準確之物質含量，我們接著結合含量總合為1與含量不為負的兩個限制條件，成為完全限制加權最小平方法。而為了更進一步應用所設計之演算法在沒有任何物質資訊的影像中，我們亦加入一個以最小平方誤差為基礎之非監督式方法，將完全限制加權最小平方法延伸為一非監督式演算法。最後，我們比較幾個高頻譜影像雜訊估計之方法，以提高本方法之偵測效能。 在本論文之電腦模擬與真實高頻譜影像實驗中，我們發現經過白化雜訊處理後之最小平方法偵測結果較好，另外亦可顯現出完全限制加權最小平方法在物質含量估計之效能也較好。 Recently, hyperspectral images are widely used for target detection in remotely sensed imagery. They take advantage of hundreds of contiguous spectral channels to uncover materials that usually cannot be resolved by multispectal images. However, the ground resolution in hyperspectral imagery is generally larger than the size of targets of interest, under this circumstance target detection must be carried out at subpixel level. Linear spectral mixture analysis (LSMA) is a widely used technique for subpixel target detection and material classification in hyperspectral image, and least squares unmixing methods are widely used to solve linear mixture problems for material abundance estimation. In this thesis, a weighted least squares (WLS) method is introduced as a generalization. When different weight matrix is applied, a certain detector or classifier will be resulted. Several previous proposed methods have been proven to be versions of WLS methods. For accurate abundance fraction estimation, a fully constrained weighted least squares (FCWLS) approach is developed by combining sum-to-one and nonnegativity constraints. In order to further apply the designed algorithm to unknown image scenes, an unsupervised least squares method is also proposed. Furthermore, several noise estimation methods are introduced, and we also compare the performance of target detection capability. A serious of computer simulation and real hyperspectral image experiments were conducted in this thesis. The experimental results showed that the noise whitening least squares method in target detection and FCWLS approach in abundance fraction estimation have better performance.
