IEEE Geoscience and Remote Sensing Magazine - June 2021 - 13

indicates that the phase gradient information is wrong,
making SB PU dependent on the integration path. Goldstein
et al. [10] provided the definition of residue, which
is that, if a loop-integration value of the phase gradients
from (4) of any 2 × 2 neighboring pixels is 2r, it is called
a positive residue; otherwise, if it is 2r,
it is called a negative
residue. To make SB PU independent on the integration
path, a residue-balance criterion is put forward in [4]. To
be specific, if the closed-path integral (i.e., the summation
of the enclosed residue polarity) is equal to zero, the
integration result is independent of the integration path.
Therefore, the residue theorem provides a sufficient and
necessary condition to make SB PU independent on path.
Figure 4(a) shows a wrapped phase image obtained from
a real InSAR data set, and Figure 4(b) displays the five
pairs of negative residues (indicated by red triangles) and
positive residues (designated by blue squares) identified
in Figure 4(a).
BRANCH CUT
The branch-cut technique is a powerful method with
the potential to provide the PU result by employing the
residue-balance criteria [10]. The main idea of the branchcut
technique is to balance the residues by deploying the
branch cut for finding the most likely reasonable integration
path to avoid the gradient error of (4). Many PU
theorems and methods operate under this principle, such
as envelope-sparsity theorems [5], [11] and Goldstein's
branch-cut algorithm [10]. Therefore, the SB PU problem
can be considered the branch-cut deployment problem.
The thorny part of the aforementioned framework is that
there are usually multiple ways to balance the residues in
practice, but InSAR cannot provide us with enough information
to guarantee which way is optimal, so the branchcut
method is also referred to as the ghost line [9].
For example, Figure 4(c)-(e) shows the different
branch-cut distributions of Figure 4(b) that were obtained
using the branch-cut algorithm [10], minimum
cost-flow (MCF) [12], and minimum spanning-tree (MST)
[13] methods, respectively. It can be observed that the
best ways for balancing the residues are multiple and
highly depend on the computing theory used by PU researchers.
Worse, sometimes, even if we know the most
desired way to balance the residues, the foundation of
computing theory still does not allow us to effectively
implement our idea, as many proposed branch-cut deployment
strategies are NP-hard, meaning that an exact
solution cannot be obtained by any method in polynomial
time unless the P-problem set is equal to the NPproblem
set [4].
In recent decades, AI-based methods have been introduced
to the field of SB PU. The SB PU method based on AI
can be roughly divided into the following two categories:
path-following PU using AI and global PU using AI, which
have totally different PU mechanisms and strategies. In the
following sections, each category is reviewed in detail.
JUNE 2021 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
AI-BASED PATH FOLLOWING
The AI-based path-following technique treats SB PU as
a local integration problem and has shown very promising
results in many works. Based on two elements of the
mature concepts for the path-following PU process (i.e.,
residue and branch cut), path-following AI-based PU
methods can be divided into two main groups: residue
estimation of AI and branch cut of AI. In the following
discussion, two groups of path-following methods of AI
are introduced in detail.
RESIDUE ESTIMATION FROM AI
As described previously, residue estimation relies mainly
on the Itoh condition-which is based on the PU researchers'
practical experience-in the traditional framework. In
recent years, several studies have suggested that, in some
fields (e.g., computer vision, natural language processing,
and so on), AI techniques demonstrate capability superior
to that of humans in terms of accumulating experiences
from different learning cases [14]. Accordingly, instead of
the Itoh condition, some researchers have already utilized
AI technology to calculate phase gradients. To the best of
our knowledge, the first such attempt was proposed in
-2
2
(a)
(b)
(c)
(d)
(e)
FIGURE 4. (a) A real interferogram. (b) The residue distribution
of (a) where red triangles represent negative residues and blue
squares represent positive residues. (c) The branch cuts generated
by the branch-cut algorithm. (d) The branch cuts generated by
MCF. (e) The branch cuts generated by MST.
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IEEE Geoscience and Remote Sensing Magazine - June 2021

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