IEEE Geoscience and Remote Sensing Magazine - June 2021 - 14

[15], where Schwartzkopf et al. proposed a neural network
(NN) for detecting phase gradient information early in
2000. Since then, there has not been any major work on
the use of NNs for phase gradient estimation.
Recently, a deep convolutional NN (DCNN) for phase
gradient estimation was proposed [16]. Referred to as a PG
network (PGNet), it detects the phase gradients by formulating
them as a three-class (i.e., the residue polarities of 0
and ±1) segmentation problem that is predicted using two
DCNNs for the vertical and horizontal directions. In this
network, three dilated convolutions [17] are used to extract
the features of the phase gradients, and a classic pixelwise
cross-entropy loss function is applied for predicting each
class at the output of the softmax classifier, defined by
loss =- ·· ,
l
/// h m
l ^ hhl^ ^^h
s
where () is the one-hot indicator that the sth pixel belongs
to the lth class^h= l 12 3and
tsl
, ,
from the groundtruth
map, which can be generated using the existing
DEM database [e.g., Shuttle Radar Topography Mission
(SRTM) digital elevation model (DEM)], and ()
psl
is the
class-conditional probability of class l on the sth pixel obtained
by the softmax function. In addition, an L2-norm
AI BRANCH-CUT DEPLOYMENT
The AI-based methods applied for branch-cut deployment
can generally be divided into two groups: AI branch-cut
preprocessing and deployment. The main goal of the methods
in the first group is to divide the whole interferogram
into several subinterferograms of smaller size based on the
c
ts log ps mi j 2
j
+
(5)
regularization term is added into the loss function to reduce
overfitting, where ()ji is the jth parameter of the
network and m is the regularization coefficient. Figure 5
depicts the detailed network architecture of a PGNet. A
similar approach for phase gradient identification is proposed
in [18], with an improved coherence map that is
also fed into the network, providing the network with a
local indication about the presence of residues.
Figure 6(a) shows a noisy simulated interferogram with
a 0.5 coherence coefficient. Figure 6(b) and (c) (47,428 and
17,690 residues, respectively) shows the residue-estimation
results obtained by the traditional Itoh condition and a
PGNet, respectively. Comparing Figure 6(b) with Figure 6(c),
it can clearly be observed that the residue distribution obtained
by a PGNet is much sparser than that obtained by
the Itoh condition, indicating that the phase gradients obtained
by a PGNet are much more accurate than those generated
by the Itoh condition.
Pixel Classification Subnetwork
Feature Extraction Subnetwork
FIGURE 5. The PGNet architecture. A wrapped phase image is given as the input, and the vertical and horizontal phase gradients at each
pixel are the outputs [16]. ReLu: rectified linear unit; Conv: convolution; BN: batch normalization.
14
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE JUNE 2021
64 × 64 × 1
64 × 64 × 1
Wrapped Phase Data
Vertical Phase Gradients
64 × 64 × 1
Horizontal Phase Gradients
Dilated Conv1
Dilated Conv2
Dilated Conv3
64 × 64 × 128
64 × 64 × 128
64 × 64 × 128
BN2
ReLu2
BN3
ReLu3
Standard Conv4
64 × 64 × 3
64 × 64 × 3
64 × 64 × 1
Softmax
Pixel Classification
64 × 64 × 128
64 × 64 × 128
64 × 64 × 128
BN1
ReLu1
64 × 64 × 128
64 × 64 × 128
64 × 64 × 128
IEEE Geoscience and Remote Sensing Magazine - June 2021

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