Exploration of component analysis in multi/hyperspectral image processing

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, p must be sufficient for data analysis. Unfortunately, in MultiSpectral Imagery (MSI) p seems to be small, while p in HyperSpectral Imagery (HSI) seems too large. Interestingly, very little has been reported on how to deal with this issue when p is too small or too large. This paper investigates this issue. When p 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 p using a set of nonlinear functions, their design rationales are completely different, particularly they are not correlated. As for a large p such as HSI, a recently developed Virtual Dimensionality (VD) can be used for this purpose where the VD was originally developed to estimate number of spectrally distinct signatures. If we assume one spectrally distinct signature can be accommodated by one component, the value of p can be actually determined by the VD. Finally, experiments are conducted to explore and evaluate the utility of component analyses, specifically, PCA and ICA using BEP and K-PCA for MSI and VD for HSI.