International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B7, 2012 
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia 
deformation velocities between two neighbouring persistent 
A(x, ,x,,t,)=k, -VAq(x,,x,)- B, mk, - Av(x, ,x, )- t, * Lr) 
t,) is the NDP of neighboring 
sat 
Where, Ad(x, +X 
persistent scatters X, and X,. f;, is time baseline of 
: Ax ; 
interferogram Z , i-1,2,...... ,N. k, sr, is 
AR sin c 
wave length, A is slant range from SAR to target, @ is 
incidence angle. VAq(x,,x,) is the difference of terrain 
errors between two neighboring PSs. B. is the normal 
UE 
A 
Av(x 2s ) is the difference of linear deformation velocities 
baseline of interferometric image 7 
k, 
between neighboring PSs. $, es (x p», ) is phase residues. 
st; 
It's the contribution of residual atmospheric delays, no-linear 
deformations and decorrelations. 
For N time serial NDPs of every pair of persistent scatters, the 
sets of N equations such as (1) are generated. Because residual 
phase $, " (x, Xf ») changes with time, the equation sets 
are a nonlinear system, i.e., rank deficiency. Under the 
condition of Du (x rad d A < 77 , the equation sets can be 
  
resolved. The VAdq(x, , x 3 and As +) can be 
estimated with bi-dimensional periodogram (Ferretti et al. 
2000a, Colesanti et al. 2003) or solution-space search method 
(Luo et al. 2011c). Then the deformation velocities of all 
persistent scatters can be deduced with the network adjustment 
(Liu et al. 2008) or by integrating along the arc of network 
(Ferretti et al. 2000a, Colesanti et al. 2003). Furthermore, the 
nonlinear deformations of persistent scatters and atmospheric 
phase screen (APS) with respect to singular SAR image or 
interferogram are filtered out from the NDPs. Finally, the time 
serial deformations of all persistent scatters and regional 
deformation field can be deduced. 
The accuracy of deformations estimated from NDPs depends 
on the degree that atmospheric delays and decorrelations are 
removed from NDPs. As long as two neighbouring persistent 
scatters defined by network are adjacent to the greatest extent 
in the geography space, most of atmospheric delays and 
decorrelation errors will be eliminated from the two 
neighbouring persistent scatters. So an appropriate network and 
Inet 
Range 
(a) (b) 
Figure 1. The PS neighborhood variation from 
geography space to image space 
    
58 
scatters. This function can be expressed as following equation, 
(I) 
optimal neighbourhood are crucial to persistent scatter InSAR. 
In order to achieve this goal, the three-dimensional persistent 
scatter Delaunay network is presented. 
3. THREE-DIMENSIONAL PERSISTENT SCATTER 
DELAUNAY NETWORK 
3.1 The problem of persistent scatter planar network 
Persistent scatter planar network is a two-dimensional network 
constructed based on image planar coordinates. The structure of 
planar network is seriously affected by SAR projection and 
image resolution. On the one hand, the azimuth resolution of 
SAR images is usually higher than slant range resolution. That 
means the real geography landscape will be stretched in radar 
flight direction, i.e., azimuth direction while landscape is 
imaged by SAR. By contrast, the target space relationship 
defined by the network established in geography space will be 
different from that derived from image space because the sites 
and space relationship of targets vary with the scene conversion 
from geography space to image space. Figure 1 indicates the 
variation of target relationship from geography space to image 
space. Figure (a) is the Delaunay network of four persistent 
scatter targets in geography space and figure (b) shows the 
Delaunay network in image space. The persistent scatter B and 
D are connected in geographic Delaunay network but the link is 
cut in image space. On the other hand, the SAR image 
distortions such as foreshortening produced by radar slant 
range projection may result in the false selection of 
neighbouring persistent scatters. As figure 2 illustrates, because 
of SAR image foreshortening, the ground distance D between 
PS, and PS, is much longer than the range d computed with 
image resolution. The foreshortening ratio ((D-d)/D) increases 
with the decrease of local incidence angle. When the local 
incidence angle is zero, foreshortening ratio gets to its extreme, 
i.e., the whole slope is imaged as a point. The foreshortening 
causes that the real geography distance of two neighbouring 
persistent scatters selected according to 1km interval is usually 
much longer than 1km. So some persistent scatter pairs with 
longer than 1km in geographic space, called false persistent 
scatter pairs exist in persistent scatter planar network 
constructed based on image coordinate system. The NDPs of 
false persistent scatter pairs remain atmosphere residues that 
will correspondingly mitigate the accuracy of persistent scatter 
InSAR. 
  
  
Figure 2. The slant range projection 
illustration of SAR