Feature Extraction from Hyperspectral Data Using ICA
203
Hyperspectral Data
x: n band~
~
Principal
Component
Analysis
~
x' : n uncorrelated
mbands to be
bands
extracted
i
Drop the lowest n-m
variance bands
i
I
x" : m uncorrelated bands
I
..
Independent
Component Analysis
..
I
u\ : m independent components
I
Fig.S.l. Independent component analysis feature extraction (leA-FE) algorithm
variance PCA band and the algorithm may fail to recover it. In that case, the
PCA step may need to be modified such that all the principal components
with nonzero variance are selected for processing by ICA. However, since the
hyperspectral data contain noise, zero variance bands are seldom found. The
ICA-FE algorithm will then reduce to the application of ICA on the original
data and will not provide any improvement in computational speed. These
issues are further discussed when an example is considered in Sect. 8.5.
8.4
Undercomplete Independent Component Analysis Based
Feature Extraction Algorithm (UlCA-FE)
Sometimes the hyperspectral images may contain independent components
with low variance. For example, in automatic target detection problem (see
Sect. 2.9 of Chap. 2), a small target in the image is generally characterized by
a limited number of pixels that will not contribute significantly to the overall