IEEE Geoscience and Remote Sensing Magazine - September 2023 - 55

known for its precise phase estimation [10], [51]. Therefore,
the simple idea is to use the most coherent interferograms
from their linked phases because the linked phases
are optimal from all possible interferometric phases. This
approach reduces the data volume by using the most informative
interferograms for further processing, thereby
allowing for efficient interferometric processing.
Let us assume that the N SAR dataset (ordered temporally)
can be divided into small batches, or ministacks, with
M images. The compressed version St of M SAR images for
the kth sequence can be determined by a coherent summation,
as follows [51], [16]:
M
t (, )(,)gm
=1
SrxS rxm
m
= /
where /, ,...,gp ppKK
==
tt
<< 6 12 M ,@ K=t
exp ()j k
t
m
is the linked
phase from M SAR images and S(r, x) is the scene complexvalued
SLC at the slant range azimuth position. The vector
g weights each image's contribution in the ministack in the
coherent summation process.
For each ministack, its compression is formed using
(16), resulting in a strong data reduction. As an example
of the algorithm's efficiency, from a stack of 90 images, we
(16)
can set M as 10 (see Figure 7). The processing will then estimate
the 10 optimum phases by using the PL technique
in (12). These phases allow us to coherently focus the stack
subset and produce a single compressed image that can
represent the 10 first images of the stack. The same procedure
will be repeated on the following 10 images until
the end of the stack, producing nine compressed images.
We note that this process has to be performed on an SHP
family basis since PL estimation can be valid only locally.
The ComSAR scheme in signal processing has benefits beyond
just reducing the computational burden. It also prevents
the need for updating and re-estimating the entire phase history
at the face of every single acquisition. The processing
scheme reduces the data volume from the entire stack to the
compressed SLCs, making storage easier. These compressed
images can then be used as a reference point to link history
ministacks with recent acquisitions and reconstruct the full
phase time series [see Figure 7(d)]. In detail, PL will be performed
on the compressed components (),St
calcal (),( ), ..., ()K12
producing a
t tt t
7
=
vector m jj j
calcal
A that contains the
calibration phases for connecting the ministacks. The datum
connection for the kth sequence is then carried out by [16]
mm j=+
tt t
k
unified
k
cal ()k
(17)
1
20
40
60
80
20 40 60 80
2
4
6
8
10
2468 10
(a)
(d)
FIGURE 7. The ComSAR algorithm. (a) A full coherence matrix in the PSDS technique. The data are divided into ministacks with 10 images
to improve the process efficiency. (b) The PL technique is employed to compress each ministack. This generates linked phases that enable
a coherent focus on the stack subset, resulting in a compressed image representing the first 10 images. This compression procedure is
repeated on the following 10 images, creating nine compressed images. These compressed images can be utilized to link prior ministacks
with new acquisitions and reconstruct the full phase time series without the need to recalculate everything. ComSAR can work with full and
compressed time series, but the (c) compressed version typically outperforms the (d) full time series version [16].
SEPTEMBER 2023 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
55
(b)
0.8
0.6
0.4
0.2
(c)
IEEE Geoscience and Remote Sensing Magazine - September 2023

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