IEEE Geoscience and Remote Sensing Magazine - June 2021 - 19

this smooth PU result excessively erodes the fringe congruency
so that the PU error shown in Figure 12(d) continuously
spreads in the bottom half of the image. In other
words, the one-step AI-based PU method can destructively
overfilter the input's phase fringes.
TWO-STEP PU METHOD OF AI
Unlike one-step AI-based PU, two-step AI-based PU formulates
the PU problem as a semantic-segmentation problem
in step 1, which takes the wrapped phase as the input
and the wrap count as the output with the conventional
cross-entropy loss function. However, because the segmentation
result obtained by step 1 cannot ensure that
all of the pixels are classified correctly, there are always
some pixels that have phase-jump errors (i.e., the error
of this pixel will be an integer multiple of 2π), so it still
needs to perform postprocessing to identify these pixels
and correct them in step 2. Then, this refined result of the
wrap count is added onto each pixel of the wrapped phase
to restore the final unwrapped phase. Compared with the
one-step AI-based PU method, the main advantage of this
group is that it can exactly guarantee fringe congruency
by using postprocessing. Spoorthi et al. proposed
PhaseNet [40] based on a fully convolutional network
[41] that can retrieve the PU result by predicting the wrap
count at each pixel of the input wrapped phase image, but
it does not work well in the event that the absolute phase
changes violently, so it needs postprocessing using clustering-based
smoothness.
Following a similar network with PhaseNet, Zhang et al.
[42] devised an additional independent network for denoising
the input wrapped phase image. Although denoising
the network is used as an auxiliary tool for the
wrap-count estimation, it still requires a postprocessing
procedure. In addition, a DeepLabV3-based PUNet
[43] has been presented to predict the wrap count in the
wrapped phase image [44]. Even though DeepLabV3 is
well known as the most powerful network in the semantic
segmentation of computer vision, a refinement step is
still inevitable. Therefore, one disadvantage of this group
is that it cannot perform well without postprocessing.
To solve this issue, PhaseNet was upgraded to 2.0 based
on DenseNet [45] (referred to as PhaseNet 2.0) [46]. The
main improvement over the original version is that the
loss function of PhaseNet 2.0 has clear PU meanings. To
be specific, besides the cross-entropy loss, which is similar
to (5), it combines residue loss and L1 loss to circumvent
postprocessing. Based on the predicted wrap count, the
unwrapped phase ()s}t
can be calculated by (3). Residue
loss is derived from the optimization model of the classic
minimum-norm PU method [4], [47], i.e., the difference
between the wrapped phase gradients and the unwrapped
phase gradients, given by
loss 11
ss, 1
-
where D ss 1- ) is the estimated wrapped phase gradient,
and D ss 1- ) is the unwrapped phase gradient.
t { (,
t
} (,
Residue {}ss=- --ss |(,) (,DD ),
/ tt |
(8)
-3
-2
-1
1
2
3
100
100
120
50
20
40
60
80
(a)
10
15
20
5
(d)
(e)
(b)
2
-2
(f)
FIGURE 12. (a) A simulated interferogram. (b) The reference unwrapped phase. (c) The PU result of (a) obtained by the one-step PU of AI.
(d) The errors between (b) and (c). (e) The rewrapped phase fringes of (b). (f) The rewrapped phase fringes of (c).
JUNE 2021 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
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(c)
2
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IEEE Geoscience and Remote Sensing Magazine - June 2021

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