IEEE Geoscience and Remote Sensing Magazine - March 2020 - 101

should be interpreted as an indication of the absolute accuracy of the measurement. On the other hand, low values
of the consistency index denote unwrapping criticalities,
which also impact the subsequent level of the model-based
analysis in Figure 2.
Moving to the model-based analysis, that is, the analysis carried out in the second step of Figure 2, an index to
discriminate points with temporal scattering persistency
properties can be, thanks to the specific use of a model,
designed in a straightforward manner. This index directly
depends on the phase noise and, therefore, can be interpreted as an index of local measurement relative accuracy
or, said differently, of scattering persistency.
The index exploited in PSI for discriminating between
reliable measurements and noise quantifies the correlation of the measured phases with the assumed model, typically dependent on the RT and (residual) MDV. Generally,
it is referred to as temporal or multi-interferogram coherence.
Its squared version can be derived from (5) with
	

f ^Ch : c pq " e j+cpq for all p and q (8)

and A = aa H , where a is the so-called steering vector associated with the phase model
	

a = e j^k z $ z + kv $ vh, (9)

where k z and k v are the (column) vectors collecting the
coefficients, depending on the distribution of the spatial
baseline and acquisition times, respectively; z is the RT;
and v is the residual MDV [4], [104]. The normalization
factor, based on the definition of A and f ^Ch , results in
F = tr ^ A h $ tr ^C h = N 2 .
Model matching or, better, the coherence degree is sought
by maximizing the coherence index with respect to unknown scatterer parameters, that is, z and v; therefore, an accurate estimator at full resolution of topography (and deformation) is provided. By measuring the phase matching with
a model, PSI naturally provides decision statistics for detecting scatterers that can be accurately localized on the ground
and monitored at the largest possible scale. The phase model
in (9) can be extended to account for further deformation
terms, such as thermal and seasonal deformation components [115], [116]. However, an increase of the model dimensionality leads to possible noise overfitting: in the context of
detection, also discussed later in this article, such overfitting
might lead to an increase in the probability of false alarm.
SAR tomography, on the other hand, provides imaging
along the elevation and velocity spectrum [9]: peaks in the
spectrum are indicators of the presence of a possible (or
even more than one) PS [104]. A decision strategy based on
SAR tomography can be adopted by performing a proper
normalization to achieve, in this case, a coherence indicator. To this end, relevant research has been carried out by
addressing the detection problem in the radar detection
framework. It was shown that, for single scatterers (as for
MARCH 2020

IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

the PSI case), the GLRT for PS detection under the Gaussian hypothesis is achieved by proper normalization of the
SAR tomogram resulting from simple beamforming [104],
t being
t , with C
[106]. More precisely, by setting in f ^Ch = C
the single-look covariance estimate, and A = aa H, with a
given by (9), the normalization factor set, in this case, is
F = tr ^ A h $ tr ^Ch = N $ tr ^Ch .
Although the PSI and GLRT (tomography-based) detectors both stem from (5), they differ in a simple but significant aspect: in PSI, only complex phases are of interest [see
(8)], but, in the tomographic case, the test exploits the entire
complex information and, therefore, includes the amplitude
information of the measured single-look covariance matrix,
that is, the matrix collecting
all of the single-look complex
interferograms. Superior perDETECTION SCHEMES HAVE
formance of the GLRT detecBEEN EXTENDED TO THE
tor over the classical temporal
MULTILOOK CASE TO
(phase-based) coherence PSI
IMPROVE DETECTION
detector has been demonstratPERFORMANCE AT THE
ed [106].
EXPENSE OF A (SLIGHT)
As for higher-order analyLOSS OF RESOLUTION.
sis, such as the detection of
multiple interfering scatterers
in layover, several detection
schemes, still stemming from the radar detection context,
have been proposed [107]. The best performing detector
that allows superresolution capabilities along the elevation
is the support-based GLRT [108], which relates the GLRT
and compressive sensing [119], [120] themes widely developed in the SAR tomography context.
Detection schemes have been extended to the multilook
case [113] to improve detection performance at the expense
of a (slight) loss of resolution. For SqueeSAR, this extension
can be simply carried out by substituting, in (8), the phase
values of the equivalent PS derived from the estimated covariance matrix [109]. For the GLRT case, this can be related
t , this time with
to the test statistics in (5) by setting f ^Ch = C
t
representing
the
multilook
covariance
estimate.
In this
C
case, the false alarm probability is dependent on the number of independent looks [113]. On the other hand, for the
CAESAR approach, the multilook sample covariance matrix is substituted with the contribution associated with the
principal component [112].
PECULIARITIES FOR LANDSLIDES MONITORING
Just like classical radar, SAR operates by exploiting the measurements of distances. This peculiarity raises many technical issues-as previously pointed out for the imaging distortion for buildings (e.g., layover)-and possible limitations
that must be taken into account in landslide monitoring.
GEOMETRICAL DISTORTIONS AFFECTING
SLOPED AREAS
SAR imaging of sloped areas, such as those typically
inf luenced by landslides, is affected by geometrical
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