INVERSION OF SYNTHETIC APERTUR,E R,ADAR (SAR) - MSpace ...

6.3.4 Principal Components Analysis
The plincipal cornponents analysis (PCA), also refelrecl as l(alhunen-Loéve
tLansfolrn, is a vety useful techlique fol the analysis of cor.related rlultiple
data sets. The PCA is lviclely usecl in cligital remote sensing to courpr.ess
the dirnensionality of rnultispectral data sets by projecting clata to an eigen
space with the objective of optimally reclucing reclundancy (e.g. Jensen l51l).
Moon eú al. [79] testecl the PCA approacli ivith SPOT clata, and showecl
that it was vely efective in the classification of surface geological features.
Masuoka et al. l75l cauied out a sirnilar PCA stucly with three SAR clata
sets.
For multiple data sets, the DN-values are often highly cor.r.elated with
each other. The rnutual relatiots of DN-values betrveen tlvo clata sets can
be measuled by covaliance matrix. Covar.iance rnatrix is defined by the joint
variance of DN-values about cornmorr mean of ts'o data sets (Jensen [51]).
Cou'elatiol coefficient is tlie latio of the covariance of trvo clata sets to the
ploduct of theil stanclard cleviatiors. Using a covariance rnatr.ix of the multispectral
data set, a new coorclinate system can be definecl so that the first
axis (or fir'st principal couponent) is alignecl to the clirectiou associated rvith
the maximum variance. The second principal cornponent is then orthogonal
to the first plincipal cornponent ancl associatecl with the lernailing rnaximum
valiance. The following principal cornponents ale clefined in a similal manner
to the second plincipal cornponent. Thus, projecting highly cor.relatecl
original clata sets to the ptincipal cornponeuts l'esults in nerv uncorr.elated
multiple clata sets. The first plincipal componelt is associatecl with the
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