線性混合模式(Linear spectral mixture analysis)已經廣泛的被應用在遙測領域上，而最小平方誤差(Least Squares)是眾多有效處理線性混合模式的方法之一。雜訊在線性混合模式中的每一各波段不一定是呈現獨立且均勻分佈(Independent and Identical Distributed，(i.i.d))，而雜訊白化最小平方誤差(Noise Whitening Least Squares，(NWFE))已經被推導證明能改善傳統最小平方誤差法的效能藉由雜訊白化處理把雜訊分佈改成i.i.d.。然而如何去估計出雜訊的共變異數矩陣仍然是一個重要的問題。已經有許多方法被提出來估計雜訊的分佈，包含空間的高通濾波器、頻率域的高通濾波器、正交子空間投影、主成份分析法和費雪線性區別法(Fisher’s Linear Discriminant Analysis，(Fisher’s LDA))。這些方法在雜訊是高斯分佈時都有很好的估計，但是當雜訊的分佈不是高斯分佈時則不理想。這篇文章中我們採用無參數加權特徵萃取(Nonparametric Weighted Feature Extraction，(NWFE))來估計雜訊的分佈並和過去的一些方法做比較。同時限制能量最小化法(Constrained Energy Minimization，(CEM))在遙測的目標物偵測上我們也加上權重改善CEM對目標光譜過於敏感的問題。最後我們並應用於MRI醫學影像，透過遙測的演算法對MRI影像做個分類與效能比較。 Linear spectral mixture analysis (LSMA) has been widely used in remote sensing applications, and the Least Squares (LS) approach is one of the most effective methods for solving LSMA problem. Since the noise in LSMA from each band may not be independent and identical distributed (i.i.d.), it has been proven mathematically that the Noise Whitening Least Squares (NWLS) will outperform the original LS by making the noise i.i.d. with the noise whitening process. But how to estimate the noise covariance matrix is remain a challenge problem. Many methods have been proposed in the past which including spatial high-pass filter, frequency domain high-pass filter, orthogonal subspace projection, principal component analysis and Fisher’s Linear Discriminant Analysis (Fisher’s LDA) based approach. They all perform well for Gaussian noise but encounter problems when the noise is ill distributed. In this study, we adopt Nonparametric Weighted Feature Extraction (NWFE) to estimate the noise distribution and compare the results. Furthermore, we also apply the weighted factor for Constrained Energy Minimization (CEM) to reduce its object spectrum sensitivity problem. Finally, we apply these methods to MRI medical images and discuss the results.
