IEEE Geoscience and Remote Sensing Magazine - June 2021 - 62

where H ,, ,
k k 123=
are the first-order difference matrices.
Furthermore, in the optimization to (6), the reweighted
strategy is utilized to update
, norm and ,11
21 ,
further improve the restored results (see " Notation " ).
FOLLOWING THE IDEA OF
NGMEET, FACTORREGULARIZED
LOW-RANK
TENSOR FACTORIZATION
ALSO UTILIZES MATRIX
DECOMPOSITION TO
DECOUPLE THE SPATIAL
AND SPECTRAL PRIORS.
EXPERIMENTAL STUDY
We choose the HS image from
DESIS, installed on the International
Space Station [54],
for our experimental study
to compare different methods
on the Gaussian- and
mixed-noise-removal tasks.
We remove the noisy bands
and select a subimage of size
400 # 400 # 200 as the clean
reference image, which is normalized
to [0, 1]. First, we
add Gaussian noise of noise variance 0.1569 to simulate
the Gaussian-noisy image and apply different Gaussiannoise-removal
methods to remove the Gaussian noise.
Furthermore, we add salt-and-pepper noise and stripes to
simulate the mixed-noisy image and apply mixed-noiseremoval
methods to remove the mixed noise. Similar to
[33], we choose the mean of peak signal-to-noise ratio
Notation
X F
X
11,
X ,12
X /12
X q
X TV
X 0
tr()X
X )
x 2
9
z
, norm to
(PSNR) over all the bands, the mean of structural similarity
(SSIM) over all the bands, and the mean of spectral
angle mapping (MSA) over all of the spectral vectors to
evaluate the restored results.
Table 2 presents the evaluation values of different methods
on Gaussian- and mixed-noise-removal results, respectively.
For the Gaussian-noise-removal task, NGmeet achieves
the best values of the three evaluation indices. However,
the gap between NGmeet and FastHyDe is limited. For
the mixed-noise-removal task, LRTDGS achieves the best
accuracy in the PSNR and SSIM values, while LRTDTV
achieved the best MSA value. Combining Tables 1 and 2,
we can conclude that, first, the spectral low-rank prior
information is important for HS restoration. Second, the
contribution of spatial low-rank prior information for HS
restoration is limited. Third, on the basis of spectral lowrank
regularization, the prior spatial and spectral smoothness
can further improve the final HS restoration results.
Forbenius norm of X, obtained by / X,
, norm of X, obtained by / X,,
21 ,
1
ij ij
, norm of X, obtained by // X ,ij ij
2
, norm of X, obtained by / ()ix,ij j
, norm of X, obtained by / ()ix,ij j
+
12 /
q
q
TV norm of X, obtained by HX HX ,hv 21
p
, norm of X, obtained by /lim ,,Xij ij
The trace of X, obtained by / X ,ii i
p 0 "
The nuclear norm of X, obtained by tr XX^
R
, norm of x, obtained by / Xj
2
j
2
The elementwise multiplication operator
The neighboring pixels of the target pixel i
h
12
/
ij ij
2
,
REMAINING CHALLENGES
To date, many nonconvex regularized methods have been
proposed to develop the low-rank and local smoothness
priors and achieve remarkable HS restoration results for
Gaussian- and mixed-noise removal. However, these methods
still face several challenges for further work, which we
summary follows.
◗ Efficiency: Although low-rank related methods have
achieved SOTA restoration results, they are time consuming.
For instance, NGmeet and LRTDGS spend
more than 10 min to process a 400 # 400 # 200 HS image.
Furthermore, the related SOTA restoration methods
always exploit multiple priors of the HS image, resulting
in confusion of the parameter chosen. Therein,
how best to reduce the model complexity and improve
optimization efficiency of the HS image restoration is a
key challenge.
◗ Scalability: Previous nonconvex-related methods always
focus on small HS image processing; however, HS images
are used to observe Earth, and the spatial size of one
scene is usually very large. How best to improve the scalability
of the restoration approaches is a key challenge.
DL provides the possibility for fast and large-scale processing
of HS images. DL approaches always rely on the
quality of training samples, and the applicable scope of
the test data is always limited. To improve the scalability,
TABLE 2. THE RESTORATION RESULTS OF DIFFERENT SELECTED METHODS FOR GAUSSIAN- AND MIXED-NOISE REMOVAL,
RESPECTIVELY.
INDEX
PSNR
SSIM
MSA
GAUSSIAN-NOISE REMOVAL
LRTA
25.99
0.7095
11.35
NAILRMA
32.81
0.9519
4.75
TDL
32.11
0.9443
4.72
FASTHYDE
33.51
0.9601
4.42
NGMEET
33.82
0.9607
4.38
MIXED-NOISE REMOVAL
LRTV
33.05
0.9459
5.06
LRMR
32.22
0.9401
4.95
LRTDTV
32.34
0.9335
4.09
LRTDGS
33.33
0.9596
4.24
LRTF-FS
33.26
0.9549
4.44
62
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE JUNE 2021

IEEE Geoscience and Remote Sensing Magazine - June 2021

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