IEEE Geoscience and Remote Sensing Magazine - June 2020 - 12

SIGNAL MODELS IN MULTIPASS SYNTHETIC APERTURE RADAR TOMOGRAPHY
STOCHASTIC SCATTERER MODEL
For the stochastic, or unconditional, scatterer model (Figure S4), the reflectivity
vector u i for a given scatterer i inside the radar cell is assumed to be stochastic
and to follow a zero-mean complex circular Gaussian distribution of (unknown)
covariance matrix C i [39], [49], [50]. This type of signal model can be applied to
volume scattering or rough surfaces with a normal vector that is not parallel to
the sensor line of sight.

FIGURE S4. The stochastic, or unconditional, scatterer signal

FIGURE S5. The deterministic, or conditional, scatterer signal

model.

is significantly different from the tomography of natural
media, where radiometric accuracy is necessary, for instance, to derive forest biomass estimates (see [55]-[57]).
The main issues that must be faced for the development
of reliable techniques to recover the signal u from interferometric acquisitions are as follows:
◗ nonuniform baseline spacing
◗ reduced number of available acquisitions (smaller than
the number of Nyquist samples)
◗ reduced elevation resolution due to a small overall baseline span
◗ presence of noise and incoherent clutter
◗ scene changes that deteriorate the coherence.
SCATTERER UNMIXING IN URBAN AREAS
We first describe methods based on the analysis of an estit of the noncentral covariance / in the "Spectral Analmate R
ysis" section; then, in the "Compressive Sensing" section, we
introduce the CS inversion method, which is applied to the
stack of single-look complex images without filtering.
SPECTRAL ANALYSIS
Numerous approaches can be found in TomoSAR to invert v and retrieve the power distribution profile p = ; u|2.
12

DETERMINISTIC SCATTERER MODEL
In the deterministic, or conditional, scatterer signal model, the reflectivity of a
scatterer remains constant during all acquisitions (Figure S5). This type of signal model can describe coherent double-bounce reflections or point scatterers [39], [50]. It is particularly well adapted for describing artificial structures
with many corners and prominent elements and is widely used for urban
areas.

Spectral analysis estimators, commonly employed in
antenna array processing, were first used to recover reflectivity profiles. Nonparametric estimators, such as
beamforming (see the "Conventional Beamforming"
section) and Capon (see the "Capon Beamforming" section), are fast and easy to compute. They are widely used
to reconstruct the volume distributions of scatterers,
such as in forest or ice. Parametric estimators consider a
reduced number of scatterers and are, therefore, better
adapted to urban areas. All estimators described here
rely on the analysis of the covariance matrix R (with
the notable exception of single-look beamforming).
This matrix is generally estimated by computing a local
spatial averaging:
L

t = 1 / w , v , v @, ,
R
L ,=1

(4)

where , identifies one of the L samples in the window that
surrounds the pixel of interest and w , is the weight associated with the , th sample. In the homogeneous regions, a
simple boxcar or Gauss-car filter can be used to perform
this estimation. Buildings and artificial structures are backscattering echoes of variable intensity.
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

JUNE 2020

IEEE Geoscience and Remote Sensing Magazine - June 2020

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