Aerospace and Electronic Systems - June 2019 - 36

Classiﬁcation of Covariance Matrix Eigenvalues in Polarimetric SAR for Environmental Monitoring Applications
referred to as textures, are statistically independent (also of x k )
positive real random variables
obeying the Gamma distribution
with scale and shape parameters m
and n > 0, respectively (the considered setting assumes m ¼ 1=n
to have a Gamma distribution with
unit mean). In what follows, it is
assumed n ¼ 2. Furthermore, the
number of iterations used to estimate the covariance structure is 5,
which ensures a satisfactory convergence level as proved in [12].
Figure 9(a) and (b) shows
the classification histograms for
K ¼ 10 and K ¼ 100 looks,
respectively. Again, as for the previous case, it turns out that a
performance gain is achieved considering a higher number of looks,
and, also that both BIC and GIC
performances overcome the AIC,
which suffers performance saturation effects instead.
In the next analysis, Pcc is plotted versus the number of snapshots.
The simulating environment is the
same as in Figure 9, but for different values of the shape parameter,
i.e., n ¼ 0:5; 1; 2; 5, and with focus
on the BIC-based estimator. Again,
each subfigure refers to a different
hypothesis for the dominant eigenvalues. From this analysis, it is clear
that the classification performance
is insensitive to variations of n, due
to the fact that the architectures for
heterogeneous environment work
in the invariant domain. Moreover,
better performance can be obtained
when K increases, since the covariance estimate becomes more and
more reliable.
As before, in Table 2, the number of decisions for each hypothesis
against K is also provided for the
Figure 7.
scenario of Figure 10. Without loss
Homogeneous case performance analysis: Pcc (%) of the three MOS rules for a simulated
of generality, the results in Table 2
scenario with K ¼ 10 (a) and K = 100 (b) looks and 104 Monte Carlo trials. Subfigures from left
refers to the case n ¼ 2 since the
to right and top to bottom refer to the different eigenvalues patterns.
performance is insensitive to the
scale and shape parameters. Again,
observing the values reported in the table, the behavior
where gk s are statistically independent N-dimensional
of the algorithm is evident also in terms of erroneous
zero-mean complex circular Gaussian vectors with covariclassification.
ance matrix C i , i ¼ 1; . . . ; 4. Moreover, t 1 ; . . . ; t K ,
36

IEEE A&E SYSTEMS MAGAZINE

JUNE 2019

Aerospace and Electronic Systems - June 2019

Table of Contents for the Digital Edition of Aerospace and Electronic Systems - June 2019

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