IEEE Geoscience and Remote Sensing Magazine - June 2020 - 37

Capon-based reconstruction, respectively, in which
(m max, e max) and (m min, e min) are the maximum and minimum eigenvalues and their corresponding eigenvectors.
The polarimetric Capon-based reconstruction application example is given using polarimetric L band airborne
data acquired by the German Aerospace Center's Experimental SAR system above a Dornstetten, Germany, test
site (see Figure 3). The MB data from 23 flight tracks were
obtained. The baselines form a quasi-uniform linear array
with an average baseline close to 20 m, and the geometric vertical resolution is approximately 2 m. The considered transect line for PolTomoSAR reconstruction contains
under-foliage objects (trucks). The tomogram of the polarimetric reflectivity in the elevation-azimuth plane is shown
in Figure 3(b), where the forest profiles (end of azimuth
line) and truck shape were extracted through the Capon
estimation approach. Taking the reconstructed unitary polarimetric-scattering pattern, the estimated a tomogram is
reported as well. The truck outside the forest was identified
with strong double-bounce reflection at the ground-truck
interaction, and the one beneath the canopy was reconstructed with the higher a values.
In the case of full-rank polarimetric information and
aiming for a second-order polarimetric-information reconstruction (that is, the polarimetric coherence, T, and
covariance, C, matrices), the model given in (14) may be
replaced by
yp =

L

/ X p ^ z lh 7 a^ z lha @ ^ z lh + w p,

double-bounce, volumetric, and surface scatterings
are set as red, green, and blue, respectively. It is interesting to observe that the ground is mainly detected by the
double-bounce scattering mechanism, while, in the upper
forest layer and canopy, volumetric scattering is dominant,
as expected. The resolution improvement from the sparsitybased technique is evident.
POLARIMETRIC BACKSCATTERING SEPARATION
In addition to the reconstruction algorithm's effectiveness, the separation and characterization of superimposed scatterers highly depends on the MB SAR sensor
configuration. Typically, decomposition is an alternative
approach that may provide a promising solution in the
scattering-mechanism separation. The scattering-mechanism decomposition effectiveness in PolSAR [40], [41] and
polarimetric interferometric SAR (PolInSAR) [42] images
has already been proved. With respect to polarimetric MB
data, different processing strategies have been presented
in the literature [17]-[19]; among them, one widely used

(20)

l=1

where X p (z l) = E {; s (z l) ; 2 v pl v @pl} ! C 3 # 3 is the second-order
polarimetric coherence or the covariance matrix (depending on the generation form of y p) of the scatterer at elevation z l. In such a case, X p can be retrieved using the following full-rank reconstructions:
X pBF ^ z l h = B @ ^ z lh R p B ^ z lh,
X pCP ^ z lh = ^B @ ^ z lh R -p 1 B ^ z lhh 1.

(21)

In (21), X pBF and X pCP are positive semidefinite matrices that
can be characterized through any classical polarimetricprocessing algorithms, such as three-component Freeman-
Durden decomposition [39].
TomoSAR and PolTomoSAR reconstructions can be
performed in a sparse-based framework. Sparsity-based retrieval is able to enhance the reconstruction quality with
respect to beamforming and the Capon spectral estimator.
The sparsity-based full-rank polarimetric reconstruction
of the coherence/covariance matrix was presented in [16].
Figure 4 provides an example of full-rank reconstruction
through different methods. In particular, an experiment is
performed that involves the Freeman-Durden decomposition in the elevation slant-range plan using TropiSAR data
[35]. The color-coded tomograms are generated through
three extracted features of the decomposition, where the
JUNE 2020

IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

(a)

(b)

(c)
FIGURE 4. The color-coded Freeman-Durden tomograms extract-

ed through full-rank reconstruction approaches. The (a) beamforming-, (b) Capon-, and (c) sparsity-based approaches. The horizontal
and vertical axes of the tomograms are related to the slant range
and elevation directions.
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IEEE Geoscience and Remote Sensing Magazine - June 2020

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