IEEE Geoscience and Remote Sensing Magazine - March 2023 - 46

The corresponding quantitative results of two inpainting
tasks are given in Table 8. Taking account of two types
of prior knowledge, TVWTR gives a significantly fortified
performance in two cases as compared with the other competing
methods. HaLRTC and LRTC are the fastest and second-fastest
among all the comparing methods.
HYPERSPECTRAL DESTRIPING
In the past three decades, plenty of airborne and spaceborne
imaging spectrometers have adopted a whisk broom
sensor or a push broom sensor. The former is built with
linear charge-coupled device (CCD) detector arrays. The
corresponding HS imaging systems scan the target pixel by
pixel and then acquire a spatial image by tracking scanning
with a scan mirror forward motion [159]. The latter contains
area CCD arrays. A push broom sensor scans the target line
by line, one direction of which is utilized for spatial imaging
and the other for spectral imaging. The incoherence of
the system's mechanical motion and failure of CCD arrays
lead to the nonuniform response of neighboring detectors,
mainly generating stripe noise. The periodic and nonperiodic
stripes generally distributed along the scanning direction
have a certain width and length. The values of stripes
are brighter or darker than their surrounding pixels. The inherent
property of stripes, i.e., ( ),g S should be considered
in the HS destriping model.
Chen et al. [58] took the first to develop an LRTD for an
MS image destriping task. The high correlation of the stripe
component along the spatial domain is depicted by an LR
Tucker decomposition. The final minimization model for
solving the destriping problem is expressed as follows:
XS Bi
min
,, ,A
s.t BB BB BI
YX SX X
2 DD
1
hh2
1
1
., ( ,,)== = 123
S A## #
T
11 22 33 i
i
i
TABLE 8. A QUANTITATIVE EVALUATION OF DIFFERENT
METHODS FOR INPAINTING.
MISSING DATA (80%)
INDEX HaLRTC LRTC
MPSNR 36.54
MSSIM 0.9391
ERGAS 4.5703
MSAD 5.3845
Time (s) 9.34
38.49
0.9555
3.7704
4.6162
23.74
50.29
TEXT REMOVAL
TVWTR HaLRTC LRTC
49.05
0.9947
1.0211
1.3792
347.46
53.39
0.9965 0.9975
1.0108
1.2424
8.38
1.1345
1.1134
24.9
TVWTR
57.31
0.9991
0.4012
0.5497
345.66
+ m S 21
,
(40)
-- ++ 1
F hz
2
where S 21, =RR R S .
z vh 2
k ji ij k
=1
=1
1
,,
Cao et al. [59] implemented the destriping task by
the matrix nuclear norm of stripes and nonlocal similarity
of image patches in the spatiospectral volumes.
WLRTR and the OLRT [37], [49] are also effective for
an HS destriping task. Chang et al. [49] simultaneously
considered the LR properties of the stripe cubics and
nonlocal patches. The OLRT algorithm is reformulated
for modeling both the recovered and stripe components,
as follows:
min 2
1
,,
j
XL Si
j
+- +
a
~ // 1
j
i
X .()n
2
di
i
j
i
j
F
TX SS
RX LL
-- + rank ()
2
2
F
t
1
rank ^hk
j
i
j
(41)
where the k rank of X denotes the rank of the matrix unfolding
placed
by <


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