IEEE Geoscience and Remote Sensing Magazine - June 2020 - 16

Because many strong scatterers are located on building
facades, a large proportion of the building information is located on vertical planes. However, defining vertical neighborhoods in the radar frame (x, r, h) is unnatural, as illustrated
in "Coordinate Systems for Synthetic Aperture Radar Tomography." In [86], the authors tackle this geometrical problem
and propose a way to introduce spatial regularization by directly inverting all of the pixels in the SAR images to retrieve
a 3D reflectivity volume expressed in ground geometry [87],
as illustrated in "Coordinate Systems for Synthetic Aperture
Radar Tomography." Equation  (4) can be rewritten, under
simplifying assumptions, as a line integral of the 3D reflectivity distribution u:

exhibits good accuracy, some parts are missing, and some
irregularities are present. This is because the height of the
scatterers in each resolution cell is estimated completely
independently from the others. To overcome this problem,
appropriate regularity constraints should be introduced.
TOMOGRAPHIC INVERSION WITH
SPATIAL REGULARIZATION
It is generally considered that parametric approaches perform better in urban areas. Taking into account the sparsity of the signal strongly helps with the localization of
human-made objects, as they backscatter strong echoes. In
addition, buildings are structured objects with generally
straight vertical walls and flat rooftops. Using these geometrical priors on the scatterer distribution may strongly
decrease the number of outliers in reconstructions but requires that tomographic reconstruction be performed for
several pixels at once.

v n (x, r) =

H/2

#-H/2 u (x, y 0 + h cos i, h sin i) exp (- jp n h) dh,
(17)

with y 0 = r sin i.

Initialize i = 1 and
P⊥ = I

Stack of SAR Images

"

Ω0

False
i ≤ KM
Preprocessing

Decide for
Hypothesis
HKM

(a)

True
"

Ωi -1 = argmax ν†PΩ⊥i -1ν

i=i+1

ν†P⊥ ν
Ωi -1

"

SLC Values at a
Given Pixel

Λi (ν) =

ν†P⊥ ν
"

ΩK

M

(b)
False

Λi (ν) < Ti
True
Decide for Hypothesis
Hi -1

End

"

(c)

K Scatterers, ΩK

FIGURE 2. The Fast-Sup-GLRT scheme, showing a (a) tomogram slice, (b) 3D height point cloud map, and (c) 3D thermal/deformation point

cloud map.
16

IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

JUNE 2020

IEEE Geoscience and Remote Sensing Magazine - June 2020

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