IEEE Geoscience and Remote Sensing Magazine - March 2020 - 13

TABLE 2. AN OVERVIEW OF PSI AND RELATED INSAR METHODS (MODIFIED FROM [22]-[24]).
TECHNIQUE

BASELINE

POINT SELECTION

SOLVER

YEAR

REFERENCE

PSInSAR

Single master

Amplitude dispersion index

Temporal coherence maximization

2001

[2]

SBAS

Small baselines

Coherence

SVD

2002

[8]

StaMPS

Single master

Phase stability

3D unwrapping

2004

[12]

STUN

Single master

SCR

Integer least squares

2006

[11]

CPT

Small baselines

Coherence and amplitude dispersion

Conjugate gradient method

2008

[14]

SPN

Small baselines

Coherence

Temporal coherence maximization

2008

[25]

QPS

Coherent baselines

QPS approach

Temporal coherence maximization

2011

[20]

SqueeSAR

Full graph

Statistical homogeneity test

PTA and temporal coherence
-maximization

2011

[26]

TCPInSAR

Small baselines

Offset deviation

Least squares

2012

[24]

PSP

Single master

Amplitude dispersion

Minimum cost flow

2014

[16]

DSI

Small baselines

Statistical homogeneity test

Temporal coherence maximization

2014

[27]

Cousin PS

Small baselines

Amplitude dispersion and cousin PS

2D + 1D phase unwrapping

2014

[28]

SPN: stable point network; SVD: singular value decomposition; PTA: phase triangulation algorithm; TCP: temporally coherent point.

points that show stable phase measurements over the period of observation (the so-called PSs). PSs are defined
as having a single dominant scatterer in a resolution cell,
often consisting of trihedral human-made structures.
Perissin and Ferretti [7] describe six main types of PSs;
PSI requires the existence of a large number of such PSs
to work properly.
PSI clearly separates the different contributions to
{ int, which allows better estimation of each contribution based on its expected behaviors. To achieve this, PSI
requires a rather large number of acquisitions, typically
more than 20, to allow for spatiotemporal analysis of each
phase contribution.
In the first step, PSI and similar techniques look for the
PSs, which, at this stage, are called permanent scatterer candidates (PSCs). There are different methods; the standard
approach is already used in PSInSAR and utilizes the amplitude dispersion index [2]. Other techniques are based
on spatial coherence [8]-[10], signal-to-clutter ratio (SCR)
[11], or combinations of amplitude dispersion and phase
criterions [12].
After selection of the PSC points, there might be processing steps to further identify stable PS points from the
PSC points, such as in the StaMPS approach [11]. In other
methods, processing may occur on the PSC, and the final
PS points might be defined via their fitness to a given model after processing. SAR interferometry is, by its very nature,
a relative measurement. Estimated deformation and height
values are best understood as relative values by analyzing
the differences in phase between points when the differences in motion, height, and so on are retrieved.
In PSI, a network is formed between the PSs, or, more
precisely, a network is first formed among a subset of the
PSs that have sufficient distribution over the image and
are estimated to be the most stable points. As shown in
Figure 7, the network of PSs is created, for example, using
a Delaunay triangulation. For each network connection,
MARCH 2020

IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

{ topo, { motion, and { residual are estimated; { residual includes
{ atmo, { orbit, and { noise.
The idea is to minimize { residual by estimating the values for Dh [see (3)] and v los [see (6)] that best fit the observed { int. In the PSInSAR approach, a periodogram with
an irregular sampling of the two dimensions, baseline and
time, is used to maximize the absolute temporal coherence c [2]:
	

1 N
argmax ( c = N / e j{int e -j^{topo + {motionh 2, (4)
∆h, v los
n=1

where { int is the phase value of differential interferogram
n, { topo is the phase of the estimated Dh according to (3),
{ motion is the phase of the estimated v los according to (6),
and N is the number of interferograms.
For PSI to work, { residual must stay below 2r along the
connections. As { residual is dominated by { atmo, { atmo must
remain below 2r, which can be fulfilled under the assumption that { atmo is changing only slowly over space, so
that, as long as the connections are short, the difference in
{ atmo of the PSs along the connection will be lower than
2r. The maximal distance is estimated to be 2 km [2], although shorter distances are often proposed.

ϕ topo
ϕ motion
ϕ residual

FIGURE 7. The triangulated network of PSs.

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IEEE Geoscience and Remote Sensing Magazine - March 2020

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