Aerospace and Electronic Systems - June 2019 - 35

Addabbo et al.

Figure 6.
Processing steps for the selection of the dominant scattering mechanism in heterogeneous environment.

scenario, even though the estimation involves the eigendecomposition for both cases.

ILLUSTRATIVE EXAMPLES AND DISCUSSION
The aim of this section is twofold. First, the nominal
behavior of the proposed classification architectures is
investigated over simulated data adhering the design
assumptions. Then, the performance is studied resorting to
measured fully polarimetric SAR data.

ANALYSIS ON SIMULATED DATA
In this section, the analysis is conducted by means of
simulated data and considering the probability of correct
classification Pcc as the performance metric. To this end,
standard Monte Carlo counting techniques are exploited
to estimate Pcc over 104 independent trials. The nominal
covariance matrices associated with the considered four
hypotheses are as follows:
C 1 ¼ Diag ð½10 10 10T Þ,
C 2 ¼ Diag ð½100 1 1T Þ,

HETEROGENEOUS ENVIRONMENT

C 3 ¼ Diag ð½100 1 100T Þ,
T

C 4 ¼ Diag ð½1000 100 10 Þ.

Data are modeled as N-dimensional (N ¼ 3, in this case)
spherically invariant random vectors (SIRVs) [34], namely

HOMOGENEOUS ENVIRONMENT

xk ¼

In the homogeneous case, data are modeled as
N-dimensional zero-mean complex circular Gaussian vectors, with covariance matrix C i , i ¼ 1; . . . ; 4.
In Figure 7(a) and (b), the classification histograms are
reported for K ¼ 10 and K ¼ 100 looks, respectively.
Each subplot refers to a specific hypothesis and the
JUNE 2019

classification performance of the AIC, BIC, and GIC with
r ¼ 3 are presented.2
Comparing the two subplots for K ¼ 10 and K ¼ 100,
it is evident that the performance improves due to a higher
number of looks in the evaluation of the MOS rules. In fact,
a high number of looks leads to better estimates of the polarimetric covariances. The histograms also highlight that both
BIC and GIC exhibit excellent classification capabilities
overcoming the AIC which tends to saturate its performance. Moreover, since BIC does not require any additional
tuning parameter as for GIC, it stands out as an effective
means for eigenvalue pattern classification.
To further corroborate the obtained results, the values
of Pcc at intermediate looks' number are shown in Figure 8
with focus on the BIC-based estimator. Each line in the
plot refers to a different hypothesis. As expected, it is clear
that the performances improve as K increases.
Since Pcc is a synthetic figure of merit, in Table 1, the
number of decisions for each one of the considered four
hypotheses is also provided as a function of K. Inspection of
the table makes clear which hypothesis the algorithm chooses in the case of selection error. For instance, H4 hypothesis
is never erroneously estimated as H1 , but for the lowest
value of K, it is erroneously classified as H2 and H3 , 568
and 413 times, respectively, over a total of 104 trials.

pﬃﬃﬃﬃﬃ
tk gk ;

k ¼ 1; . . . ; K

(35)

The choice of the GIC parameter comes from the fact that it returns
the best performance with respect to the cases where 1 r 3.
Moreover, values of r greater than 3 could lead to worse classification performance since the penalty term becomes more and more
dominant with respect to the fitting term.

IEEE A&E SYSTEMS MAGAZINE

Aerospace and Electronic Systems - June 2019

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