IEEE Geoscience and Remote Sensing Magazine - March 2019 - 41

in InSAR signal processing. First, we review the established single-baseline (SB) PU methods and then describe
innovative PU techniques and concepts related to multibaseline (MB) PU and large-scale (LS) PU. In addition, we
discuss several numerical processing examples of these
PU techniques. It is our hope that this review will provide
guidelines to future researchers to enhance further PU algorithmic developments.
OVERVIEW OF SYNTHETIC APERTURE RADAR
INTERFEROMETRY
InSAR is a powerful and well-established remote-sensing
technique used to measure many important geophysical
parameters, e.g., surface height of topography or ground
deformation. For a given scene, InSAR detects absolute
phase changes between two or more SAR acquisitions from
slightly different positions [1]-[4]. The working principle of
InSAR is illustrated in Figure 1, where h (s) is the terrain
height of the sth pixel, r (s) is the slant range of the target
from the master channel of the sth pixel, i is the incidence
angle, and B is the normal baseline.
Based on the InSAR geometry, we know the range difference 9r is
9r =

B
·h (s).
r (s)· sin (i)

(1)

Furthermore, 9r is also equal to
9r = 2rm·m ·} (s),

(2)

where m is the carrier wavelength and } (s) is the absolute phase change of the sth pixel. Moreover, m is the
transmit-receive factor, where m = 1 represents the bistatic mode and m = 2 the distributed mode. As Figure 1
shows, the absolute phase information can be converted
to geophysical parameters. However, due to the limitation of the practical SAR system's signal transmitting and
receiving models, we can directly extract only the absolute phase modulo 2r, which is the principal phase value
of the absolute phase called the wrapped phase. Under this
condition, the obtained phase must be unwrapped before
further use. In fact, a drawback as well as fundamental
challenge of InSAR is that the desired absolute phase information is ambiguous [5].
The InSAR measurement of a target, i.e., the wrapped
phase, can be given by
{ (s) = } (s) - 2k (s) r,
where { (s) ! (-r, r] and k (s) ! integer,

REVIEW OF SINGLE-BASELINE PHASE UNWRAPPING
The PU problem in SB InSAR is a 2D PU problem,
which means the input of the InSAR PU problem is a 2D
wrapped phase matrix, called the interferogram in the rest
of this article. Figure 2(a) shows a filtered realistic interferogram (the imaged area is from the Mount Etna volcano, Italy). The problem definition of the SB PU is that
the SB PU method plans to recover the absolute phase of
each pixel from a given interferogram. SB PU is now a
mature research field: the first research about SB PU can
be traced back to the 1970s [6]. Figure 3 illustrates the statistics for journal and conference publications on SB PU
(from Web of Science [14]). As Figure 3 shows, we can see
that, because it is a relatively mature research topic, there

B

θ

r (s )

(3)

where { (s) is the wrapped phase of the sth pixel and
k (s) is called the ambiguity number of the sth pixel. We
can see that the wrapping operation is a nonlinear process, and } (s) can be achieved only by removing the 2r
ambiguity from } (s). Hence, the technique of 2r -ambiguity removal, i.e., PU, is one of the most important
march 2019

processing steps of InSAR [6]. In fact, besides InSAR,
PU is also the core processing step for many other interferometric measurement techniques, such as magnetic
resonance imaging [7]-[11] and optical interferometry
[12], [13].
From (3), it is apparent that the difficulty of PU mainly
arises because it is an ill-posed inverse problem. Specifically, there are two unknowns [ } (s) and k (s) ] in (3), so
we cannot use only (3) to uniquely estimate the absolute
phase. In other words, multiple solutions of } (s) can be
achieved by one { (s) with different k (s)s. To find the
unique PU solution, we have to make some assumptions
or add some extra information.
In this technical review, we survey the established SB
PU methods first. Then, we review the innovative PU
techniques and concepts related to MB PU and LS PU developed in the past decades. In addition, we point to the
most likely future challenges and research directions in
the PU domain. Our expectation is that this survey will
motivate and help researchers to design more creative PU
techniques in the future.

ieee Geoscience and remote sensinG maGazine

∆r
h (s )
Pixel s
FIGURE 1. The working principle of InSAR.

41
IEEE Geoscience and Remote Sensing Magazine - March 2019

Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - March 2019
