IEEE Geoscience and Remote Sensing Magazine - June 2021 - 59

device (a charge-coupled device) during the conversion
from electrons to the final image [15]. The stripes are generated
in the HS data collected by the pushbroom HS sensors
[16]. Due to weather conditions, the obtained HS data
always suffer from the clouds and cloud shadows [17]. In
addition, HS images are subject to signal-dependent [18],
multiplicative, impulsive, and Laplace noises, and so on.
Furthermore, in this article, we follow the mainstream and
focus on the Gaussian-noise-removal [19], [20] and mixednoise-removal
problems [21], [22] (see Figure 5).
Since the 1980s, researchers have paid attention to HS
noise analysis. For example, maximum noise fraction
(MNF) transformation [23] noise-adjusted principal component
analysis (PCA) [19] is utilized to extract high-quality
components for the subsequent classification and rejection
of low-quality components. Following mainstream gray/
color-image denoising in computer vision, various state-ofthe-art
(SOTA) technologies have been deployed, such as
wavelets [24], sparse representation [25], [26], TV [20], [27],
nonlocal means processing [28], [29], low-rank matrix representation
[21], [22], [30], [31], tensor representation [32]-
[34], DL [35], [36], and so on.
The nonconvex regularized methods have also been developed
for HS image restoration. In [21], the HS images are
assumed to be corrupted by the additive noise, including
Gaussian noise, stripes, deadlines, pixel missing, impulse
noise, and so on. The observation model is formulated as
Y XN NGS
=+ +
,
(3)
where Y represents the observed noisy image, X stands
for the latent clean image, NG
is the Gaussian noise, and
NS is the sparse noise, including stripes, deadlines, pixel
missing, and impulse noise (see " Nomenclature " ). Typically,
when sparse noise NS
is omitted, the model (3) is degraded
to the Gaussian-noise-removal problem. From [21],
the low-rank property exploration of clean image X has attracted
much attention and achieved SOTA HS image-denoising
performance [29], [34]. Generally, the mainstream
comes from two points. First is how best to explore the
low-rank property of clean image .X Until now, spectral
[21], [30], spatial [33], [37], and nonlocal low-rank properties
[29], [32] have all been well studied. Furthermore,
how best to balance the contribution of different low-rank
properties has also been a key problem [29], [38]. Second,
the low-rank constraint of X formulates a nonconvex optimization
problem. Therein, how best to efficiently solve
the rank-constraint nonconvex problem is another key
issue. In the next section, we review several outstanding
works and illustrate how they formulate low-rank modeling
and how they solve the nonconvex problem.
(a)
(b)
(c)
FIGURE 4. Examples of different noise types from the HS images
observed from airborne and spaceborne sensors. (a) The HYDICE
urban HS data. (b) The AVIRIS HS data. (c) EO 1Clean
HS Image
Noise
LRTA
HYPERION HS data.
GAUSSIAN-NOISE REMOVAL
In this section, five methods are selected to represent the SOTA
HS image Gaussian-noise-removal approaches. These methods
utilize different low-rank matrix/tensor decomposition
NAILRMA
TDL
FastHyDe
NGmeet
(a)
Clean HS Image
Noise
LRMR
LRTV
LRTDTV
LRTDGS
LRTF-FS
(b)
FIGURE 5. The different methods used for noise-removal results. (a) The results of the different methods used on the Guassian noise-removal
experiments (R:70, G:100, and B:36). (b) The results of the different methods used on the mixed-noise-removal experiments (R:31, G:80,
and B:7). FastHyDe: fast HS denoising; NGmeet: nonlocal meets global; LRTV: low-rank TV; LRTDTV: low-rank tensor decomposition with TV;
LRTDGS: low-rank tensor decomposition with group-sparse regularization; LRTF-FS: factor-regularized low-rank tensor factorization.
JUNE 2021 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
59
Mixed Noise
Gaussian Noise
IEEE Geoscience and Remote Sensing Magazine - June 2021

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