IEEE Geoscience and Remote Sensing Magazine - March 2019 - 53

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FIGURE 17. (a) The LS TerraSAR-X InSAR data. (b) The PU result of the LS SNAPHU method. (c) The PU result of the GAMMA LS MCF

method. (d) The PU result of the fast PU method for LS interferograms [19].

PU solutions of the SNAPHU method. In addition, by
recalculating the branch-cut information of a simplified
network, the approximative global LS PU solution to the
SB L1-norm PU method can be achieved [106]. Moreover,
[107] used a simulated annealing-technique-based splicing strategy to parallelize the SB Goldstein's branch-cut
method for the LS PU problem. Finally, [26] used the information of a triangulation network to combine the local
PU results of the SB MCF PU method.
A PU experiment of the LS SNAPHU method in [105]
and the GAMMA LS MCF method in [26] will be used to
better explain the characteristics of the first group of methods. Figure 17(a) is an LS TerraSAR-X interferogram (18,000
× 20,000 pixels). Figure 17(b) is the PU result of the LS
SNAPHU method with the interferogram tiled, which is
implemented by algorithm designers and whose running
time is 27,363 s with a 3.2-GHZ central processing unit
(CPU) frequency, and Figure 17(c) is that of the GAMMA LS
MCF method, whose running time is 3,180 s with the same
CPU frequency. From Figure 17(b) and (c), we can clearly
see that the mosaic phenomenon exists in the PU results:
the mosaic phenomenon of the LS SNAPHU method is far
weaker than that of the GAMMA LS MCF PU method but
is still obvious and marked by the rectangular box in Figure 17(b). In addition, the algorithm running time of LS
SNAPHU is relatively long. From this experiment, we could
conclude that the methods in the first group sometimes
cannot guarantee consistency between local and global PU
solutions. However, the benefit of the first group's methods
is that the subinterferogram size is a user-defined parameter, so the first group's methods can easily control peak
memory consumption based on the hardware condition.
The methods in the second group put their computation load on the tiling step. Based on the clustering characteristic of the residue distribution or the quality map of the
input interferogram, such methods make use of the clustering-analysis technique to divide the input interferogram
into unfixed and irregular subinterferograms and maintain consistency between local and global PU results. The
envelope-sparsity theorem provided in [102] explains theoretically why this kind of LS method can guarantee consistency between local and global PU solutions. Because
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the clustering analysis-based tiling strategy has already
guaranteed that the PU solution for each subinterferogram
is independent of the others, we can safely unwrap each
subinterferogram and use a simple splicing strategy (i.e., a
process such that most of the tile differences between each
two neighboring subinterferograms are zero) to combine
SEVERAL OF THE LATEST
the PU results of all the subInSAR TECHNOLOGIES
interferograms together.
REqUIRE THAT THE PU
In [44] and [19], e.g., two
ALGORITHM BE ABLE TO
methods are proposed, the
outlier-detection method for
PROCESS MULTIPLE
LS PU (ODLS) and the fast
INTERFEROGRAMS
PU method for LS interfeSIMULTANEOUSLY.
rograms (FLS), for LS SB L0 norm and L1-norm PU problems based on the residue-clustering characteristics. In
addition, [108] put forward a quality-map-partition-based
LS SB PU method for P-band ultrawideband InSAR technology. By making use of the residue-clustering characteristics, the convex hull algorithm has also been applied for
LS SB PU [109].
To describe a residue-clustering framework [102], each
residue i can be considered as a clustering object, whose clustering radius is denoted as b i . When the distance between
residue i and residue j is smaller than Function(b i, b j), where
Function (b i, b j) is a similarity measure function, these
two residues will be clustered together. If all of the residues
satisfy the clustering termination condition, the algorithm
will stop. Otherwise, the clustering radii of the residues that
do not meet the termination condition will be increased,
and then the residues will be clustered again.
Figure 17(d) illustrates the PU result of Figure 17(a)
obtained by the FLS method in [19] (the running time
is 2,578 s with 3.2-GHZ CPU frequency). Comparing
Figure 17(d) with (b) and (c), it is clear that the PU result of
FLS seems the most seamless among these results (i.e.,
almost no mosaic phenomenon). Furthermore, the FLS
method has the fastest execution speed among the three
algorithms. This comparison reveals that the methods in
the second group can better ensure consistency between
local and global PU solutions. However, the limitation of
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