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In: Wagner W., Szekely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7,2010, IAPRS, Vol. XXXVIII, Part 7B 
Interferometry, Small BAseline Subset, Coherent Pixel 
Technique, which will be introduced chronologically in some 
detail, together with the differences and relations between each. 
2.1 Least Square database approach (LS approach) 
After analyzing the phase stability of some man-made features, 
S.Usai et al (Usai et al., 1997,1999,2000) presented a new 
approach, known as Least Square approach (LS), for the long 
term monitoring of terrain deformations with D-InSAR. This 
method uses a database of interferograms, and by solving all the 
deformation velocities as a unique least squares problem 
provides a chronologically ordered sequence, describing the 
evolution of the deformation pattern in time (Usai, 2002). 
2.1.1 Main principle 
The input for the least squares adjustment is a set y=[Ii,...,I N ] of 
N unwrapped interferometric deformation maps(i.e., the 
unwrapped interferograms are compensated for topographic and 
flat-earth phases), all coregistered at subpixel level, generated 
from M SAR images taken at days x=[d 1 ,..., d M ]. The day di 
corresponding to the first image is taken as reference and the 
deformations at each of the other (M-l) days relative to this day 
considered as solutions of the problem: 
y=Ax (1) 
where in x the element d] not been considered. 
In the system matrix A, each row corresponds to an 
interferogram, while the columns correspond to the days. For 
interferogram I k —Idi-Idj» the values on row k are all zero except at 
columns i and j, being +1 and -1 respectively and A an 
incidence like matrix, directly depending on the set of 
interferograms generated form the M SAR images. 
The unweighted least squares solution x of Eq.l is 
straightforward: 
x=(A T A)-'A T y Qx=(A T A)-‘ (2) 
2.1.2 Some notes on LS approach 
The LS approach has been applied to measure terrain 
displacements in the period 1993-1999 at the Phlegrean Fields 
(Naples, Italy), using a set of 20 ERS-1/2 SAR images, and 43 
interferograms generated(Usai, 2002; Usai, 2003). The authors 
made use of an external DEM to obtain the differential 
interferograms and found that residual topography had caused 
systemtic effects in the data. In addition, during the processing, 
a closed-loop method was used to detect and remove image- 
and interferogram-related biases. In fact, according to Usai, 
(Usai, 2001) two kinds of biases can be identified: the image- 
related ones, like for example those caused by atmospheric 
disturbances; and the interferogram-related ones, i.e. those 
which have been produced in the interferometric combination of 
two images, most probably by phase-unwrapping errors. 
2.2 Permanent Scatterer (PS) 
The Permanent Scatterer technique, developed at the 
‘Politecnico di Milano’ (Milan, Italy) (Ferretti et al., 1999; 
2000; 2001), is the first of a family of similar advanced 
interferometric techniques-Permanent Scatterer Interferometry 
(PSI). 
Given N+l images, a set of N differential interferograms is 
generated with respect to a single master. High temporal and 
normal baseline interferograms (affected by a high decorrelation 
noise) are, thus, part of the dataset. The approach focused on 
privileged image pixels that, even in these ‘extreme conditions’, 
still exhibit a low noise term, thus the so-called Permanent 
Scatterers. With PS technique, pixels are selected from the 
study of its amplitude stability along the whole set of images 
(typically >30). Therefore, the maximum resolution of the SLC 
images is preserved (Ferretti et al., 2001) 
After PS candidates selection, a linear model is adjusted to the 
data to estimate the deformation linear velocity and possible 
DEM errors for each PS Candidate. Then the atmospheric phase 
screen (APS) for the master image and the nonlinear motion 
contribution and APS for each image are computed through a 
spatio-temporal filtering. After estimation and removal of all the 
APS superimposed on the data, one can identify more PSs and 
repeating the previous steps allows getting the whole 
deformation time series and average LOS displacement rate of 
every single PS, and a refining DEM with sub-metric precision 
of the exact height of the object corresponding to the PSs. 
2.3 Small BAseline Subset (SBAS) 
The Small Baseline Subset (SBAS) approach, proposed by 
Berardino et al. (2001; 2002), extends the Least Squares 
approach (Usai, 2001; 2002; 2003; Lundgren et al, 2001) to the 
case of multiple small baseline acquisition subsets. The key 
point, in addition to the use of multi-look interferograms, is that 
the data pairs involved in the generation of the interferograms 
are carefully selected in order to minimize the spatial baseline, 
thus mitigating the decorrelation phenomenon and topography 
errors. The Singular Value Decomposition (SVD) method is 
applied to link otherwise independent SAR datasets separated 
by large baselines. The SBAS method was originally used to 
investigate large scale deformations with spatial resolution of 
about 100m* 100m, calculating the time sequence deformation 
and estimating DEM error and the atmospheric artifact in a 
similar way as PS. O.Mora et al (O.Mora et al., 2002) promoted 
a complementary approach, utilizing two different sets of data 
generated at low (muliti-look) and full resolution (single-look) 
respectively, to monitor localized deformation. The former are 
used to identify and estimate possible atmospheric phase 
artifacts and low-wavenumber deformation patterns based on 
SVD SBAS method or CPT(Mora et al., 2003); the latter to 
detect, on the high-resolution residual phase components, 
structures highly coherent over time like buildings, rocks, lava 
structures, etc. 
2.4 Coherent Pixels Technique (CPT) 
Developed by O.Mora et al (2003), original CPT gained its first 
use (Mora et al., 2001) in the long-term subsidence monitoring 
of an area of small town in Spanish, choosing the temporal- 
coherence as criterion for permanent scatterers selection only to 
make flexible the SAR images requirement in PS. The results, 
utilizing seven SAR images, turned out to be satisfactory and 
coincided well with the DGPS measurements. 
Recently, CPT has been improved (Blanco et al., 2007; Duque 
et al., 2007) into an operational advanced technique for terrain 
deformation mapping, in terms of linear and nonlinear 
deformation extraction, robustness with DEM error, thus 
allowing DEM refining, and atmospheric phase screen (APS) 
removal. P.Blanco et al (2008) concluded this approach and 
detailed the main steps, such as optimal interferogram sets 
selection, coherent pixels selection, linear and nonlinear blocks 
for a full deformation extraction. The related algorithms consist 
of Delaunay triangulation and Minimum Spanning Tree (MST) 
for best combination of interferograms selection, Conjugate 
Gradient Method (CGM) for Phase Unwrapping, multi-layer for