依據前人理論推導証明，雜訊白化最小平方誤差﹝Noise Whitening Least Squares、NWLS﹞ 可改進傳統最小平方誤差﹝Least Squares、LS﹞的效能，而如何精確估計雜訊分佈是NWLS最重要的一部份。NWLS它是物質含量估計及次像素﹝Sub-Pixel﹞分析方法，用最小平方誤差法估計線性光譜混合模型中物質含量，也引用加權矩陣投影及兩個物質含量限制條件。加權矩陣為雜訊白化矩陣，雜訊白化是將原高光譜影像資料空間投影到新資料空間，雜訊形成相同且獨立分佈﹝Identically and Independent Distributed、i.i.d.﹞，也會讓雜訊局限於多維單位圓之內。雜訊為隨機﹝Random﹞信號，每一種雜訊來源可視為一個隨機變數，根據中央極限定理，雜訊隨機變數總和，其分佈趨近於高斯分佈。雜訊估計和雜訊模式估計差異在於前者估計資料點雜訊成份，後者則估計雜訊分佈。在論文中使用不同估計雜訊方法進行實驗，將高頻信號視為估計的雜訊部份，計算雜訊互變異矩陣描述雜訊分佈。實驗結果証明使用巴特沃斯高通頻域濾波器﹝Butterworth High-Pass Filter﹞其估計最好，最能符合雜訊原始分佈。雜訊分佈估計越符合，NWLS估計物質含量越精確，估計影像信號也是會越精確且能提升訊雜比﹝Signal to Noise Ratio、SNR﹞。在實驗中也有比較雜訊消減和雜訊白化對信號估計的改善程度比較，結果是雜訊白化改善效果大於雜訊消減。 It has been proved that the Noise Whitening Least Squares (NWLS) can significantly improve the performance of the original Least Squares (LS), and how to better estimated the noise distribution is the most important step in NWLS. It is a method for target abundance estimation base on sub-pixel analysis. It solves linear spectral mixture model by least squares solution with two constraints and the weighted matrix. The weighted matrix is the noise whitening matrix. In the noise whitening processing, it projects the original hyperspectral space to a new data space. The noise will form identically and independent distribution (i.i.d.) after the projection. After the noise whitening projection and it will be distributed in unit circle in multidimensional space. The noise is a random signal. The sources of noise can be viewed as random variables. According to the Center Limit Theory, the distribution of the sum of N independent random variables will become gaussian distribution when N goes to infinity. The difference between estimation of noise and noise model is that; the former estimate the noise value in data point, and the latter estimate the distribute of noise by its covariance matrix. In this thesis, we compare different noise estimation methods, which estimation noise by the high frequency part of the signal and the experiment results shows the butter method high-pass frequency filter gives the best results. If we has better estimation of noise, the NWLS can estimate the abundance more accurately. In this case, we will have better estimation of the signal and higher signal to noise ratio (SNR). We also compare the performance of de-noising and noise whitening processing. The result shows the noise whitening processing is better than the de-noising.
