成份分析法在遙測影像處理中可以見到許多之應用。主成份分析和獨立成份分析法是常見到之兩種技術，它們通常在訊號處理中扮演重要角色。主成份分析法是藉由二階統計量去解相關後得到分析資料之主成份，而獨立成份析法則是採用衡量資料之統計獨立性得到獨立成份。

不幸地是，若利用成份分析法對多頻譜磁振造影像處理而言，維度L太小無法提供足夠訊息作分析。有趣的是過去文獻亦少有探討，因此本論文提出利用核函數主成份分析和擴維度兩種技術來探討維度L和成份p之間關係。

最後由實驗結果可發現，SVM並沒有因為用維度擴張而增加辨識率。這主要是因為ROI選取太小的緣故，無法看出維度擴張的效用。但是並不代表維度擴張沒有它的功能。根據文獻的報告，當BEP與SVM用整張影像為ROI時它的辨識率明顯增加。因此本論文藉由不同大小之ROI（20×20、32×32、64×64）證明的確ROI太小時會無法顯示出擴張維度之效用。

Component Analysis (CA) has found many applications in remote sensing image processing. Two major component analyses are of particular interest, Principal Components Analysis (PCA) and Independent Component Analysis (ICA) which have been widely used in signal processing. While the PCA de-correlates data samples via 2nd order statistics in a set of Principal Components (PCs), the ICA represents data samples via statistical independency in a set of statistically Independent Components (ICs).
However, in order to for component analyses to be effective, the number of components to be generated, L must be sufficient for data analysis. Unfortunately, in MultiSpectral Imagery (MSI), such as magnetic resonance imaging (MRI), L seems to be small. Interestingly, very little has been reported on how to deal with this issue when L is too small. This thesis investigates this issue. When L is too small, two approaches are developed to mitigate the problem. One is Band Expansion Process (BEP) which augments original data band dimensionality by producing additional bands via a set of nonlinear functions. The other is a kernel-based approach, referred to as Kernel-based PCA (K-PCA) which maps features in the original data space to a higher dimensional feature space via a set of nonlinear kernel. While both approaches make attempts to resolve the issue of a small L using a set of nonlinear functions, their design rationales are completely different, particularly they are not correlated.
Finally, experiments are not conducted to improving the results of SVM by using BEP and K-PCA methods. It is because of too small ROI, and unable to evaluate the utility of BEP and K-PCA. According to the reference, it was improved the classification result of SVM when using the BEP method as pre-processing. Therefore, this thesis used different sizes ROI (20×20, 32×32, and 64×64) to prove that ROI is too small to evaluate the utility of BEP and K-PCA.

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