The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
interval; however, the multiple of 27i to be added to the 
measured phase is never known. The step where the phase is 
converted from the ambiguous interval to the unambiguous real 
number is called phase unwrapping. Classically, this is 
performed in 2D array of the interferogram and the criterion is 
set for the unwrapped interferogram to have as little phase 
jumps (more than 2n difference between the neighbouring 
pixels) as possible. However, this criterion is set artificially and 
the result may be unreliable, especially in low-coherent areas 
(where the phase value is also considered unreliable). 
We propose a method suitable for processing of stack of data 
where phase unwrapping errors are estimated iteratively in the 
third dimension - time. The method is described in section 4. 
3. DATASETS 
We focus on the North-Bohemian brown coal basin where 
mining has been performed for several centuries, using different 
mining methods. In past, lots of deep mines were opened - 
however, these areas are expected not to subside any more. 
Currently, most coal is being mined using open-pit mines, 
which are then mostly recultivated to forests, lakes, agricultural 
fields etc. 
However, there are some areas where an artificial object was 
built on a waste dump, such that the well-known Ervenice 
corridor (between Most and Chomutov), or the road between 
the villages Kost’any and Mstisov (near Teplice). We decided to 
map deformations in these two areas using InSAR. 
Figure 1. Area of interest in North Bohemia 
For processing data acquired by ERS-1 and ERS-2 satellites 
during 1996-2000 are used. Due to bad coherence in the most 
areas, only parts of the scene is processed and analysed, namely 
roads built up on a waste dump, where the coherence is high 
enough to give predicative results. 
4. ITERATIVE ADJUSTMENT 
We generate as many interferograms as possible from the 
available data. That means each scene is paired with each other, 
with previous resampling all scenes to a selected master. Then, 
after the topography is subtracted and the interferograms are 
spatially filtered and unwrapped, the most coherent points are 
selected from the interferograms (most of them are contained in 
the object we are monitoring) and then the most coherent 
interferograms are selected, which enter further processing 
(about 100). 
In order to make the phase unwrapping unambiguous at least in 
ideal cases, the assumption of spatial phase continuity is 
adapted. It means that the phase difference between two 
neighbouring pixels is in the (-re, +7i) interval. In our case the 
assumption is helped by the fact that the interferogram contains 
only deformation signal (and noise). The points, where the 
assumption is not fulfilled, can be easily found out and are 
called residues. Between individual residues, branch cuts are 
created and the unwrapping paths are not allowed to cross them. 
Branch cuts creation is an ambiguous problem and its solution 
is not trivial. Several methods are applied for this problem, 
some of them even use different information, such as weights 
(coherence), scene magnitude (possible layover effects when 
unwrapping topography data) etc. When the area to be 
unwrapped contains low-coherent regions, which causes the rest 
of the area to break up into separated regions, only one of this 
regions is unwrapped (the one that contains the reference point, 
at which the unwrapping starts). 
First step to be performed is referencing each interferogram to a 
single point, which is ideally stable. This step is performed to 
eliminate a large part of the atmospheric influence, together 
with other systematic errors which may originate e.g. from orbit 
errors. The reference point is ideally as close to the area of 
interest as possible and should be stable, because of relative 
nature of interferometric measurements. 
The following processing is performed for each point 
individually, starting at the reference point and when selecting 
the following point, the point that has the most already 
processed neighbouring points is selected. 
Interferograms doubles and triples are constructed. In these 
cycles, the phase sum must be close to zero [l](Usai, 2004). 
This is one of the criteria for the iterative adjustment - the other 
is the unique standard deviation, which is required to be as 
small as possible. The interferograms, for which the sum is 
larger than a threshold, are then excluded (for the particular 
point). The phase sum is first computed using complex 
multiplication, i.e. the unwrapping errors are not counted for in 
this step. 
The unwrapping errors are then estimated from the 
neighbouring points (the unwrapping errors are assumed to 
change slowly in the space). For the first point, zero 
unwrapping errors are assumed (this is the unwrapping seed and 
the reference point so the phases are zero or close to zero here). 
Then, adjustment is performed, modelling that each 
interferogram is a difference of two scenes. The aim of the 
adjustment is to estimate the phases of the scene, which can be 
directly computed into deformations. After the initial 
adjustment, the residues are checked and if any of them is larger 
than ±7i the phase is corrected by an appropriate multiple of 2n 
(only one residue at a time). While the unique standard 
deviation is getting lower, this process is continued. When all 
residues are smaller than ±n or the unique standard deviation is 
higher, the phase sums in cycles are checked (now also 
considering unwrapping errors). If the cycle conditions are 
filled, the adjustment is finished for the point. If not, the space 
of ambiguities is searched for the best solution; however, it is 
not possible to search the whole ambiguity space because of its 
size - the search is limited to about 1000 searches, and the