IEEE Geoscience and Remote Sensing Magazine - March 2020 - 97

classical single-pair DInSAR. Starting from N available SAR
images, a subset of differential SAR interferograms, out of
all possible combinations, is generated by imposing a hard
limitations on the maximum temporal and spatial baseline
separations: hence, the name small baselines. Such baseline
constraints are introduced to limit the detrimental effect of
decorrelation and limit the RT phase contribution: the latter can be problematic at the PU stage.
The phase vector { in (3) is related to the collection of,
say, M interferometric phase values stacked in the vector
D{ through the matrix D:
	

D{ = D{, (4)

where D is the M # N incidence matrix [5] describing the
network formed by the acquisition and interferograms: M
is larger (typically two or three times) than N so as to introduce a redundancy in the interferogram stack generation. It
is evident from the linear character of (4) that the elements
of D{ are assumed to be unwrapped.
In their classical implementations, SCI approaches exploit a spatial averaging (multilook) of the interferograms
to further limit decorrelation and generally increase the
signal-to-noise ratio by filtering out noise contributions, at
the price of spatial resolution loss [5]. This operation also
allows access to multitemporal information about the distribution of the spatial coherence, which is exploited to select the sparse grid of points where phase measurements are
assumed to be reliable enough for the processing, especially
for the unwrapping.
The estimate of { is achieved by inverting the linear system in (4) through the pseudo-inverse D @ of the matrix D
after the introduction of an additional equation for setting
the reference of the measurement to an initial zero condition. Proper regularization must be addressed under the
unfavorable circumstance of separated subsets in the interferograms network leading to the ill-conditioning of matrix
D; see [5] for more details.
Thanks to the redundancy, the residual interferometric
phase (originated by PU errors) between the original interferograms and the interferograms generated from the
least-square (LS) solution of (4) is exploited to measure the
reliability of the unwrapping process: this point, concerning the derivation of reliability indexes associated with the
provided results, is detailed in the "Sequential Analysis and
Decision Strategies" section.
A remark about the use of a model for the topographic
and (nonlinear) deformation terms is now in order. The latter term is often modeled as a sum of linear (with respect to
time) and nonlinear components, thus introducing the socalled deformation mean velocity (DMV) and a (residual)
nonlinear component. RT and DMV models can be used in
modern multitemporal methods to improve PU [94], [95].
These models can be also helpful for isolating and filtering
the deformation time series from the disturbance components in (3). However, a general characteristic of the SCI
MARCH 2020

IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

techniques is the fact that the whole time series [not only
the nonlinear deformation (NLD) component] is retrieved,
thanks to the absence of direct use of a matching indicator
between the signal and a "structured" component associated with a (RT- and DMV-dependent) model.
SCI techniques are well suited to the monitoring of socalled distributed scatterers, that is, ground textures characterized by a spatial uniform backscattering within the
resolution cell and whose extension is, typically, larger
than the resolution cell. Unlike PSs, distributed scatterers
are much more affected by temporal and spatial decorrelation, the latter induced by the angular diversity of the acquisitions. Such an aspect is of interest for the investigation
of landslides and unstable slopes located in places where
the absence of natural and/or anthropic PSs could affect the
monitoring capability.
On the contrary, in the presence of distributed bare soil,
spatial averaging can filter out decorrelation sources [5],
[87]. Moreover, since the multilook induces a resolution
loss, interferograms in the native azimuth/range grid can be
downsampled downstream of the average operation, thereby reducing the data volume and computational demand,
or, equivalently, for mapping large areas. This feature may
permit, at the first level of analysis, the implementation of
cost-effective and quick assessment procedures for the detection of unstable slopes over wide areas, such as on a regional scale.
FULL-RESOLUTION INTERFEROMETRIC ANALYSIS
AND MULTIDIMENSIONAL IMAGING
The multilook strategy enables an approach to landslide
monitoring over wide areas, but the low-resolution characteristic of the processing limits the detailed analysis possible at the stage of single-building risk analysis and in the
case of a limited extent of the unstable slope with respect to
output resolution.
The PSI technique, first introduced in [4] and [96], revolutionized SAR interferometry by introducing the concept
of joint coherent processing of multiple acquisitions. It is
now available in several commercial [97]-[99] and freely
available software programs. PSI demonstrated, for the first
time, the ability to estimate and compensate for APS and
introduced the use of temporal coherence as an indicator
at the maximum available resolution of a match, in the
complex domain, of data acquired over multiple orbits to a
phase model related to RT and DMV.
PSI approaches exploit (on the "same level" [100]) all
of the possible interferograms; that is, no limitation on the
baselines is instilled. Therefore, PS approaches are devoted
to the monitoring of scatterers that are both concentrated
in space (i.e., whose dimension is smaller/comparable with
respect to the resolution cell to retain coherence, even over
nonnegligible angular imaging variations, such as spatial
baselines) and, above all, hold coherence or better "persistency" of the scattering over the whole temporal observation interval. The temporal coherence-that is, the data
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IEEE Geoscience and Remote Sensing Magazine - March 2020

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