IEEE Geoscience and Remote Sensing Magazine - March 2013 - 25
image resolution. Recent approaches exploit both PS and
coherent distributed scatterers simultaneously in order to
increase the number of valid pixels, and hence achieve a
larger coverage of the measurement [94]. The selection of
valid pixels is, in any case, an intense topic of research,
where the objective is to find as many as possible valid
pixels at the best spatial resolution [39], [95]-[100].
The non-linearity of the problem, i.e., the wrapping of
the phases, is also addressed differently. Some techniques
perform the phase unwrapping of the individual interferograms on a sparse grid to turn the problem linear and
ease the forthcoming filtering steps [69], [91], while others
exploit phase differences between neighboring pixels working in the complex domain (non-linear optimization),
being nevertheless required to perform an integration
process afterwards [92], [97]. More advanced approaches
perform 3-D phase unwrapping, i.e., including the time
variable, hence gaining some more robustness in comparison to the previous approaches [101]-[103].
Once the pixels have been selected, a first estimation
of { topo and a given deformation model, usually linear,
is performed simultaneously. After removing these two
components from the image stack, a new set of residual differential interferograms is obtained, which mainly contain the residual motion of the scatterer, the atmospheric
phase screen (APS), and phase noise. By exploiting the frequency response of the APS both in time (high-pass) and
space (low-pass), it can be estimated and removed from
the image stack [17], [69]. Finally, the residual motion
remains, which added to the previously estimated deformation, delivers the temporal evolution of the deformation for each pixel.
Figure 15(b) shows an example of the estimated mean
deformation velocity over Mexico City using the PS technique with an image stack of 36 TerraSAR-X stripmap
images. As an additional product, an accurate DEM is
obtained (see Fig. 15(c)). With current high-resolution
spaceborne sensors like TerraSAR-X or COSMO-SkyMed,
the topography retrieval turns into an interesting alternative to Lidar for accurate DEM generation of cities in a
global scale [104]-[106]. Furthermore, the estimated APS
can be also exploited for atmospheric modeling and water
vapor retrieval [54], [86].
V. Polarimetric SAR Interferometry
Polarimetric SAR Interferometry (Pol-InSAR) is based
on the coherent combination of single- or multi-baseline
interferograms acquired at different polarizations [18],
[35], [107]. Combining the potential of radar polarimetry
to identify individual scattering processes and to amplify
or attenuate them with respect to each other with the sensitivity of SAR interferometry to the spatial variability of
vertical structure parameters allows to build up a unique
observation space for the characterization of the vertical
distribution of scattering processes in natural and artificial
volume scatterers.
march 2013
ieee Geoscience and remote sensing magazine
A. Interferometric Coherence:
Information Content
The key observable in Pol-InSAR measurements is the complex interferometric coherence (that includes both, the
interferometric correlation coefficient and interferometric
phase) measured at different polarizations. As discussed
in Section IV-A (see (30)), c depends on instrument and
acquisition parameters as well as on dielectric and structural parameters of the scatterer [52], [77], [108]. The geometric baseline decorrelation term c Geo expresses the
angular dependency of the scattering reflectivity in terms
of amplitude and phase.
Due to the slightly different incidence angles induced by
the spatial baseline, the projection of the 3-D scatterer into
the two interferometric SAR images is different. Accordingly, c Geo expresses the (horizontal and vertical) spectral
correlation properties of the scatterers reflectivity [52].
Assuming the scatterers reflectivity to be locally invariant
in the horizontal direction, c Geo can be further decomposed into
c Geo = c Az c Rg c Vol . (36)
Range and azimuth spectral decorrelation c Rg and c Az are
caused by the different projection of the scatterer groundrange and azimuth spectrum into the two images forming
the interferogram. The difference in range, as explained
in section IV-A is due to the slightly different incidence
angles while the difference in azimuth is due to different
Doppler centroids. In the case of distributed scatterers the
non-common spectral parts decorrelate when forming the
interferogram. Both contributions can be compensated
(i.e., c Rg = 1 and c Az = 1) by
Polarimetric SAR
the so-called common specinterferometry allows
tral band filtering, i.e., by filthe characterization
tering the range and azimuth
bandwidth of the two images
of the vertical
at different central frequenstructure of natural
cies excluding the non-comand artificial volume
mon parts [52], [79].
scatterers.
Volume decorrelation c Vol
is the decorrelation caused
by the different projection of
the vertical component of the scatterer reflectivity spectrum
into the two interferometric SAR images. It contains therefore information about the vertical structure of the scatterer
[52], [108]. Indeed, c Vol is directly related to the vertical distribution of scatterers F (z) in the medium through a (normalized) Fourier transformation relationship [35], [52]
hV
#
c Vol = exp (ik z z 0)
F (zl ) exp (ik z zl ) dzl
0
, (37)
hV
#
F (zl ) dzl
0
25
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