Aerospace and Electronic Systems - June 2019 - 30

Classiﬁcation of Covariance Matrix Eigenvalues in Polarimetric SAR for Environmental Monitoring Applications

Figure 2.
PolInSAR covariance symmetries classification of BioSAR II L-Band data [13].

polarimetric image pixels share the same covariance but
different power levels. In this paper, a more general
framework is presented and assessed on different datasets. Specifically, given the pixel under test, the number
of dominant eigenvalues for the pixel under test is classified exploiting the pixels in its neighborhood (i.e.,
looks) assuming that the same PCM is shared among the
pixels (homogeneous environment) or, due to reflectivity variations of the scene, the covariance matrix exhibits different scaling factors from pixel to pixel
(heterogeneous environment). These scaling factors are
representative of the power levels raising from different
30

backscattering strength [12]. In the latter case, original
data are replaced by a maximal invariant statistic (MIS)
to remove the dependence on the nuisance parameters.
Moreover, the statistical characterization of the MIS is
provided along with suitable estimates of the unknown
parameters. For both homogeneous and heterogeneous
environment, the classification problem is, then, formulated as a multiple hypotheses test with nested hypotheses [27]. It is important to observe that in the presence
of nested hypotheses, the classical maximum likelihood
approach (MLA) might return erroneous classifications.
For this reason, the model-order selection (MOS) rules

IEEE A&E SYSTEMS MAGAZINE

JUNE 2019

Aerospace and Electronic Systems - June 2019

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