IEEE Geoscience and Remote Sensing Magazine - March 2023 - 38

known as Gaussian noise, when massive photons are collected
and with a signal-dependent variance in a low-flux
regime [136].
Imaging results are degraded to varying degrees by various
sources in different imaging conditions, resulting in a
variety of HS restoration issues, such as HS image denoising,
HS image blurring, HS image inpainting, and HS image
destriping. Here,
M (·) denotes different linear degradation
operators for different HS restoration problems:
1) When ( )M X keeps X constant, i.e.,
TX ).SN=+ +
M ( ),X X= (20) is
=+
reformulated as an HS destriping problem (T XS)
or HS denoising problem (consider only Gaussian noise
TX N=+ or mixed noise
2) When (·)M
is a binary operation, i.e., one for original
pixels and zero for missing data, (20) turns into an HS
inpainting problem.
3) When (·)M is a blur kernel, also called a point spread
function (PSF), (20) becomes an HS deblurring problem.
The HS restoration task is to estimate recovered HS images
X from the given HS images .T This ill-posed problem
suggests that extra constraints on X need to be enforced for
the optimal solution of
X . These additional constraints reveal
the HS desired property and various types of HS prior
information, such as nonlocal similarity, spatial and spectral
smoothness, and subspace representation. The HS restoration
problem can be summarized as
min Mf g
-- xm
X
() ++ (21)
F
2
() ()
2
1 TX SX S
where x and m are regularization parameters and ( )f X
and ( )g S stand for the regularizations to explore the desired
properties on the recovered X and sparse part
S , respectively.
Various regularization aspects are summarized
and divided into different types for systematic learning in
the " Rank Minimization Approaches " section. For example,
sparsity measurement is critical in HS reconstruction
tasks. Willett et al. [142] reviewed the state of the art of
HS image models, with an emphasis on sparse regularizations.
Das et al. [143] designed an efficient criterion to
explore multiway sparsity for HS noise removal. Das et al.
[144] developed a novel semisupervised parameter-free
algorithm for library pruning that made use of sparsity
measures, which verified the computational efficiency
and proficiency of the proposed method in the presence
of noise.
HYPERSPECTRAL DENOISING
Observed HS images are often corrupted by mixed noise,
including Gaussian noise, salt-and-pepper noise, and
dead line noise. Several noise types of HS images are
available in Figure 5. Figure 5(a) shows an urban dataset
containing mixed noise, especially heavy stripes and dead
lines. These two types of noise have a directional and
linear structure, destroying the inherent structure of the
original HS image. As shown in Figure 5(b), the Indian
Pines dataset is corrupted by salt-and-pepper noise and
Gaussian noise. The salt-and-pepper noise damages the
spectral characteristics of the original signal and causes
Internal Factors
HS Sensor
Solar
Environmental
Factors
Noise
Cloud
Spectral
Dimension
Blur
Spatial
Dimension
Spatial
Dimension
Restored
Stripe
FIGURE 4. HS image restoration.
38
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE MARCH 2023
IEEE Geoscience and Remote Sensing Magazine - March 2023

Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - March 2023
