IEEE Geoscience and Remote Sensing Magazine - June 2020 - 35

in the Capon reconstruction, where the ground is hardly
detectable in the L band case [Figure 2(c)] compared to the
P band version [Figure 2(d)]. Although this feature has the
greatest impact on the ground backscattering, it influences
the tomographic reconstruction of any target below the
vegetation's top layer.
The complex vertical-reflectivity profile ; c ; 2 in (6) refers to the contribution that actually returns to the radar,
thus incorporating any power loss due to propagation.
Any quantitative evaluation of the reflectivity estimated
through tomography should take this issue into account.
Ideally, the attenuation of each vegetation layer should be
known and compensated for; however, a direct estimation
from the data represents a strongly ill-posed problem.
Similar considerations apply for structural estimations,
as any "hole" in the forest might be due to the strong
attenuation of the targets above. This problem is less dramatic when using the HH polarimetric channel or very
low-frequency signals. In such cases, due to the lower attenuation, the forest layer can be imaged from the top to
bottom, thus offering the possibility of locating the top
and bottom edges to estimate the underlying topography
and forest height.
POLARIMETRIC TOMOSAR
In this section, some standard processes for the characterization of forest environments through polarimetric TomoSAR (PolTomoSAR) are reviewed. The polarization diversity in TomoSAR is expected to enhance focusing ability and
facilitate the characterization of the electromagnetic (EM)
behavior of complex media's different components.
Generally, the polarization information contained in
the waves backscattered from the scene is known to be related to geometrical structure and orientation as well as the
structures of the observed objects [37]. In particular, radar
polarimetry employs the full-vector nature of polarized

EM signals; by striking a wave to an object, the previously
mentioned characteristic target information can be represented in a 2 × 2 scattering matrix, S. In the case of having
horizontally (h) or vertically (v) polarized antennas, and
on the basis of (h, v), the fully polarimetric response from
the target in a specific azimuth-range resolution cell can
be given by
y hh y hv
E,
S =;
y vh y vv

(12)

where the complex scattering coefficient y pq indexed as
p, q = (h, v) represents the EM signal and is emitted through
the polarization channel q and received on channel p. In
the case of interchanging the transmitting and receiving
antennas' roles, such as with the reciprocity theorem, the
scattering matrix is symmetric; that is, y hv = y vh [38].
In polarimetric SAR (PolSAR), S may be vectorized as
the two known target scattering vectors; that is, the Pauli (k)
and lexicographic (X) feature vectors which are given by
k=

1
6y hh + y vv y hh - y vv 2y hv@T = sv k,
2

X = 7y hh 2 y hv y vvA = sv X,
T

(13)

where v =; s ; 2 denotes the polarimetric span or reflectivity
of the scatterer and v k, v X ! C 3 # 1 are unitary polarimetric
target vectors; that is, v @k v k = 1 and v @X v X = 1. The deterministic scatterers' complete process can be described by k and
X, while, for the naturally distributed scatterers present
in forested areas, the target vectors may follow a random
property if the wavelength of the SAR system is smaller
than that of the resolution cell. For this case, the target
vectors can be modeled by the complex circular Gaussian probability-density function, where the second-order
statistic can be represented by the polarimetric coherence,
T = E {kk @}, and covariance, C = E {XX @}, matrices.

(a)

(b)

(c)

(d)

FIGURE 2. (a) The reconstructed tomograms for the specified range line in HH polarization for the L band with a beamforming solution.

(b) The reconstructed tomograms for the specified range line in HH polarization for the P band with a beamforming solution. (c) The reconstructed tomograms for the specified range line in HH polarization for the L band with a Capon solution. (d) The reconstructed tomograms
for the specified range line in HH polarization for the P band with Capon solution.
JUNE 2020

IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

35
IEEE Geoscience and Remote Sensing Magazine - June 2020

Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - June 2020
