IEEE Geoscience and Remote Sensing Magazine - June 2021 - 16

(BCNet) problem]. After generating training samples of
branch cuts based on the optimal branch-cut connection
criterion (OPT-BC), which is designed by minimizing the
difference between the reference unwrapped phase and the
unwrapped phase from the branch cuts, the BCNet applies
a lightweight DCNN to predict the branch cuts in the input
residue image, where the network produces image representations
with low resolution to spatially summarize the
input residue image and maps the low-resolution feature
images to the full input resolution image for the branchcut
connection. Based on the class-conditional probabilities
obtained by a softmax function, the pixelwise, weighted
cross-entropy loss is applied as the objective function
for training the network, i.e.,
loss / ts ws log ps
1
=-s
1
1
ts
ws log ps
2
2
(( )· ()·( ())
(( ))·( )· (( ))),
(6)
where t(s) is the binary, true-label indicator of the branchcut
pixel [i.e., ()
ts 1= means that pixel s belongs to the
branch-cut pixel in the training data set]; and () andws1
ws2 () are the weights, which can control the thickness of
the generated branch cuts. Figure 9 shows the detailed network
architecture of a BCNet.
Figure 10 provides an example of the branch-cut learning
result of a BCNet. Figure 10(a) is a simulated noise-free
interferogram. Figure 10(b) is the reference unwrapped
phase of Figure 10(a). Figure 10(c) is the noise-polluted interferogram
of Figure 10(a), in which a fully noisy area is
added (the coherence in the noisy area is 0, and that in the
rest areas is 0.85). Figure 10(d) is the residue distribution
of Figure 10(c). Figure 10(e) is the reference branch-cut
connection result obtained by OPT-BC using Figure 10(b)
and (d). If we use Figure 10(b) with different noise levels to
generate the training samples utilized to train the BCNet
using
_ ^^ ihh the branch-cut connection re=
ws
ws 1512
,
sult obtained by the BCNet is shown in Figure 10(f).
Although the employed training data set does not include
Figure 10(d) and (e), compared with Figure 10(e), we
can see that the BCNet correctly recognizes that the residue
set needs to be balanced. In addition, the branch cuts
generated by the BCNet are nearly identical to the ones
shown in Figure 10(e), only fatter, which looks like the
BCNet uses mask cuts [27] to balance the residues (especially
in noisy areas with high residue densities). It is worth
mentioning that the branch cuts generated by the BCNet
can balance most of the residues because the generated
branch cuts are similar to those obtained by the OPT-BC.
However, theoretically, a BCNet cannot ensure that all of
the residues are balanced, so postprocessing is still necessary.
This is because, even if a few residues are unbalanced,
a discontinuous phase gradient error could spread to the
whole image [4]. Under this condition, an existing, modelbased
branch-cut method can be applied to balance the
rest of the unbalanced residues (a BCNet and its branchcut
postprocessing are jointly abbreviated as the BCNet-PU
method). Compared with the whole number of the residues
in the interferogram, the number of unbalanced residues
after BCNet processing is much smaller, so the postprocessing
step will be performed quickly.
Figure 11 presents a case study on the performance of
BCNet-PU compared with other competing model-based SB
PU methods. Figure 11(a) shows a real TerraSAR-X add-on
for DEM (TanDEM-X) interferogram (1,000 × 1,000), and
Figure 11(b) shows the corresponding unwrapped phase
obtained by SRTM DEM. Figure 11(c)-(f) displays the unwrapped
result obtained by the branch-cut algorithm [10],
MCF [12], PU maxflow (PUMA) [32], and BCNet-PU [26]
methods, respectively. Figure 11(g)-(j) shows the corresponding
errors between Figure 11(b) and Figure 11(c)-(f).
IEEE Geoscience and Remote Sensing Magazine - June 2021

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