IEEE Geoscience and Remote Sensing Magazine - March 2023 - 40

and nonconvex relaxation. Although these pure LRTD approaches
utilize the LR prior knowledge of HS images, they
are hardly effective to suppress mixed noise, due to the lack
of other useful information.
OTHER PRIORS-REGULARIZED LOW-RANK
TENSOR DECOMPOSITION
Various types of priors are combined with an LRTD model
to optimize the model solution, including nonlocal similarity,
spatial sparsity, spatial and spectral smoothness, and
subspace representation.
NONLOCAL SIMILARITY
An HS image often possesses many repetitive local spatial
patterns, and thus, a local patch always has many similar
patches across an HS image [147]. Peng et al. [148] designed
a tensor dictionary learning (TDL) framework. In Figure 6,
an HS image is segmented into 3D full-band patches
(FBPs). Similar FBPs are clustered together as a 4D tensor
group to simultaneously leverage the nonlocal similarity
of spatial patches and spectral correlation. TDL is the first
model to exploit the nonlocal similarity and the LR tensor
property of 4D tensor groups, as demonstrated in Figure
6(b). Instead of a traditional alternative least-squaresbased
tucker decomposition, Bai et al. [30] improved a
hierarchical least-squares-based nonnegative tucker decomposition
method. Kong et al. [31] incorporated weighted
tensor norm minimization into the Tucker decompositions
of 4D patches.
Differing from [30], [31], and [148], other works [32],
[33], [34], [35], [36], [38] obtained a 3D tensor by stacking
all nonlocal similar FBPs converted as matrices with
a spatial mode and spectral mode [Figure 6(d)]. Based on
a nonlocal similar framework, Dong et al. [32] proposed
a Laplacian scale mixture-regularized LRTA method for
denoising. Xie et al. [33] conducted a tensor sparsity
regularization, intrinsic tensor sparsity (ITS), to encode
the spatial and spectral correlation of nonlocal similar
FBP groups. With the nonlocal similarity of FBPs, X is
estimated from its corruption T by solving the following
problem:
mi ()n XT2
K +c
X
iiX
F
2
(25)
where the sparsity of a tensor X is ( )( )#
and A is the core tensor of X via the Tucker
K =+ -
P =1
i rank()X()
N
i
decomposition X A BBB= ### Xue et al. [34] pre11
22 33
.
sented a nonlocal LR (NLR)-regularized CP tensor decomposition
algorithm. However, the Tucker and CP decomposition-related
methods are subject to heavy computational
burden issues.
Chang et al. [35] discovered the LR property of nonlocal
patches and used a hyper-Laplacian prior to model
additional spectral information. He et al. [36] developed
a new paradigm, called the nonlocal meets global (NGmeet)
method, to fuse the spatial nonlocal similarity and global
spectral LR property. Chen et al. [38] analyzed the advantages
of a novel TR decomposition over Tucker and
CP decompositions. The proposed nonlocal TR (NLTR)
decomposition method for HS image denoising is formulated
as
min 2
1
XG,ii
TX s.t. XG
ii F ii
2
-=U ([]).
(26)
The nonlocal similarity-based tensor decomposition methods
focus on removing Gaussian noise from corrupted
HS images and unavoidably cause a computational burden
in practice.
SPATIAL AND SPECTRAL SMOOTHNESS
HS images are usually captured by airborne and spaceborne
platforms far from Earth's surface. The low measurement
accuracy of imaging spectrometers leads to low spatial resolutions
of HS images. In general, the distribution of ground
objects varies. Moreover, high correlations exist among
different spectral bands. HS images always have relatively
smoothing characteristics in the spatial and spectral
domains.
An original TV method was proposed by Rudin et al. [8]
to remove the noise of gray-level images, due to the ability
to preserve edge information and promote piecewise
smoothness. HS image smoothness can be constrained
by either an isotropic TV norm or an anisotropic TV norm
[149]. Obvious blurring artifacts are hardly eliminated in
the denoised results of the isotropic model [150]. Thus,
anisotropic TV norms for HS image denoising are investigated
in this article. We take the Washington, D.C. (WDC)
X ttA 10
Group
Matching
Unfolding
Stacking
Group 1 Group 2
FIGURE 6. Nonlocal LR-tensor-based methods.
40
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