IEEE Geoscience and Remote Sensing Magazine - June 2021 - 61

difference and utilize well-developed color/MS denoising
methods for HS image denoising, Zhuang et al. proposed
the fast HS denoising (FastHyDe) [41] method by translating
the HS image to low-dimensional reduced images via SVD.
With this translation, various SOTA color/MS image-denoising
methods, such as wavelets [42] and block-matching 3D
[41], are used to denoise the reduced image. Finally, the denoised
reduced image is translated back to the denoised HS
image via inverse SVD. Generally, under the framework of
FastHyDe, the HS image noise-removal task is linked to the
development of color/MS image noise-removal tasks.
NONLOCAL MEETS GLOBAL
A spatial nonlocal low-rank regularizer can produce SOTA
HS image noise-removal performance [179]. However,
as the spectral number increases, the time cost of nonlocal
related methods also increases significantly [32], [38].
The nonlocal meets global (NGmeet) method also tries to
translate the HS image to the reduced image and utilizes
a nonlocal, low-rank method to denoise the reduced image.
Different from FastHyDe, NGmeet tries to perfect the
framework by iteratively eliminating the error caused by
SVD on the noisy HS image and automatically estimating
the spectral rank of the reduced image.
MIXED-NOISE REMOVAL
In the following sections, we select five representative methods
for the HS image mixed-noise removal. These methods
are based on the observation model in (3). We focus on the
nonconvex low-rank regularizer of original image
properties of these five methods are summarized in Table 1.
images, and so TV is introduced to explore the spatial smoothness.
Generally, low-rank regularization and TV are the two
most studied regularizers, and the combination of them to
produce SOTA HS image mixed-noise removal is becoming
popular. Most of the following works try to either improve the
low-rank [47], [48] or smoothness modeling [33], [49], [50] of
the HS image to further improve the restoration accuracy. To
further combine low rank and TV, the low-rank exploration
of the HS difference image is also developed [51], [52].
X . The
LOW-RANK MATRIX RECOVERY
Zhang et al. first introduced the observation model (3) to
analyze complex HS noise [21]. Low-rank matrix recovery
(LRMR) tries to restore the original clean image X from
the noisy image via the low-rank and sparse decomposition
model as follows:
min -- mmcard(),
YX NX NSS
2
X
F 12
++ (5)
rank ()
where YX N,, S are the reshaped matrices of YX NS
,,
along
the spectral dimension, respectively, and m1 and m2 are
the parameters that trade off the contributions of
and nonzero elements card() N .S
rank() X
LRMR utilizes the " GoDec "
algorithm [43] to alternatively update the nonconvex
constraint X and NS
and finally obtains the restored image.
To improve the efficiency of the optimization to (5),
several nonconvex substitutions, such as the reweighted
nuclear norm [31], c-norm [44], smooth-rank approximation
[45], and normalized f-Penalty [46], are further
developed to exploit the spectral low-rank property of X.
LOW-RANK TV
Low-rank TV (LRTV) is based on the idea that the spectral lowrank
property is not enough to describe the property and HS
JUNE 2021 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
LOW-RANK TENSOR DECOMPOSITION WITH TV
Low-rank tensor decomposition with TV (LRTDTV) [48]
tries to improve upon LRTV by utilizing low-rank tensor
decomposition to exploit the
low-rank property of HS images,
while spatial-spectral TV
(SSTV) explores the spatial and
spectral smoothness simultaneously.
Although LRTDTV
achieved better mixed-noiseremoval
results, as reported
in [48], the spatial rank utilized
in LRTDTV is much larger than
that of the spectral rank. This
is mainly because the spatial
low-rank property of HS images
is not as important compared
to the spectral low-rank
property. From another side, the spatial, nonlocal low-rank
regularization proved to be more efficient [40] than the spatial
low-rank property for the HS restoration problem.
LOW-RANK TENSOR DECOMPOSITION
WITH GROUP-SPARSE REGULARIZATION
Low-rank tensor decomposition with group-sparse regularization
(LRTDGS) [33] [180] also utilizes low-rank tensor
decomposition to exploit the low-rank property of HS
images. Differently, LRTDGS explores the group sparsity
of the difference image instead of SSTV in LRTDTV. From
the mathematical modeling, LRTDGS utilizes weighted
,
21 ,
norm regularization to fulfill the row-group sparsity of the
difference image.
FACTOR-REGULARIZED LOW-RANK
TENSOR FACTORIZATION
Following the idea of NGmeet [29], [181], factor-regularized
low-rank tensor factorization (LRTF-FR) [53] also utilizes matrix
decomposition to decouple the spatial and spectral priors.
From one side, the spectral signatures of the HS image are
assumed to be of smooth structure. From another side, the reduced
image is assumed to have a group-sparse structure in the
difference domain. The optimization model of the LRTF-FR is
min YX NX
XN
XNS
,
++
=
mm
-- +
2
S
2
2 /
k
# H
1
61
F 13 3 21
m
2
kk F
3
# H
,
S 11, ,
(6)
THE NOISE INTENSITY IN
DIFFERENT BANDS OF THE
HS IMAGE IS DISSIMILAR, A
BIG CHALLENGE IN HS
IMAGE GAUSSIAN-NOISE
REMOVAL; THIS IS
MITIGATED BY THE NOISEADJUSTED
ITERATIVE
STRATEGY.
IEEE Geoscience and Remote Sensing Magazine - June 2021

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