IEEE Geoscience and Remote Sensing Magazine - June 2020 - 8

limited number of available acquisitions, uneven baseline
spacing, low SNRs, and poor achievable height resolutions. These issues can be partly resolved using advanced
processing techniques and, possibly, including available
a priori information. The use of a priori information has
already proven effective for multibaseline interferometric techniques [13], [44]-[47], since it allows the height
of a given pixel to be estimated by properly taking into
account the information contained in the surrounding
pixels, in such a way that it mitigates the overall impact
of phase noise.
The extension of these techniques to TomoSAR is not
an easy task, due to the difficulty of defining the neighborhood of a given scatterer in 3D space, as discussed in
the "Tomographic Inversion With Spatial Regularization"
section. The effort required to include the a priori information is, however, rewarded by its potential to provide
high-resolution digital elevation maps (generated using
wide-coverage spaceborne sensors) that show improved
accuracy and are described by continuous surfaces or
high-density point clouds, possibly evolving in time with
subcentimeter accuracy. This feature is attractive for 3D
mapping and infrastructure monitoring in urban areas
due to the presence of high-elevation buildings and humanmade structures (for instance, bridges, decks, and
roads) on small spatial scales. Therefore, the development
of these types of advanced techniques has mainly focused
on urban applications.
In this article, we first present an overview of tomographic methods and then discuss the regularization and
postprocessing schemes that are particularly suited to the
accurate reconstruction of urban areas. Finally, we describe
techniques for estimating the slow motion of each scatterer
for applications in urban monitoring.

TomoSAR SIGNAL MODEL
In TomoSAR, multiple-pass images are acquired in an interferometric configuration (Figure 1). The phase recorded at
a given SAR pixel for each track depends on several factors:
1) the location of the scatterers relative to each other within the resolution cell [the red volume in Figure 1(a)]
2) position of each antenna along the tracks
3) possible slow motion of the scatterers between each image acquisition
4) atmospheric phase screen seen at the time of each image
acquisition
5) misregistration due to different samplings of the SAR
images
6) thermal noise on the antenna
7) focalization issues.
TomoSAR exploits the relation between the phase and
the geometrical location of the scatterers (factors 1-3); see
"Multidimensional Imaging in Multipass Synthetic Aperture Radar Tomography." Factors 4-7 are nuisance phenomena, which are strongly reduced by proper preprocessing; see "Data and Results." Estimation and removal of the
atmospheric phase screen is an important step in InSAR in
general and, particularly, in TomoSAR [48].
"Multidimensional Imaging in Multipass Synthetic Aperture Radar Tomography" derives a geometrical model to relate
the location (and possible motion) of scatterers within a resolution cell and the complex amplitude in the (preprocessed)
single look complex (SLC) stack. At a given pixel v n of the nth
SAR image, a coherent mixture of the echoes backscattered by
all scatterers contained in the elevation direction is collected:
H/2

vn =

#

-H/2

u(h) exp;-

4jrb n
4jr
h+
T (h)E dh.
mR 0
m r

(1)

z
N th Track
Nth

r

N

x

N th Image

b

h

n

b

n th Track

Masters Track

n th Image
Mas
Master Image

(a)

(b)

FIGURE 1. The geometry of TomoSAR: (a) the acquisition geometry and (b) the coregistered SAR images.

8

IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

JUNE 2020
IEEE Geoscience and Remote Sensing Magazine - June 2020

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