IEEE Geoscience and Remote Sensing Magazine - March 2022 - 11

system and can acquire digital images in hundreds of narrow
and continuous spectral bands, spanning the visible
to infrared spectrums. Different from a traditional image
containing only three bands (red, green, blue) and a multispectral
(MS) image containing several broad bands, an
HSI usually includes hundreds of spectral bands with much
higher spectral resolution. The high spectral resolution and
rich spatial image information of HSIs make them suitable
for determining the subtle differences between similar
materials as well as useful in many fields, such as military,
agriculture, and mineralogy. However, their high dimensionality
and complex spatial structure also bring new challenges
in data processing. Advanced HSI processing should
consider both spectral and spatial information, especially
its specific characteristics, such as spatial homogeneity,
spectral low rank, and sparsity.
Although an HSI has very high dimensionality, it has
intrinsically sparse and low-rank structures due to the
very high correlation between spectral channels and spatial
pixels [1]. The SR and LRR-based methods have proven
to be powerful tools for HSI processing [2], [3]. Given
an overcompleted dictionary, SR aims to approximate
a measured signal with a linear combination of a small
number of dictionary atoms. The compact and sparse
signal-representation pattern helps to reveal the intrinsic
structural information embedded in the data and to
simplify the subsequent analysis and processing [4]. This
makes an SR method competitive in many HSI applications,
such as denoising with the assumption of sparse
additive noise [5], [6], unmixing with the assumption of
sparse abundance matrix [7], [8], classification with the
assumption of sparse coefficients [2], and so on. The high
spatial similarity of HSIs implies the low-rank characteristic
of the data [1]. An LRR model seeks the lowest rank
representation among all the samples. It can capture the
global structure of an HSI and provide an efficient method
for robust subspace segmentation from corrupted data.
LRR can be used to recover sparse noise or identify outliers
[3] and can also be used for dimension reduction or
subspace clustering [9], [10].
Due to the use of sparse and low-rank properties of HSI,
SR and LRR-based methods have shown excellent performance
for HSI processing. In this article, we mainly aim to
review related research and provide guidelines and inspiration
for the future development of HSI processing. Table 1
lists the taxonomy of the HS, SR, and LRR methods discussed
in this article.
LOW-RANK AND SR FOR HSI DENOISING
The nature of HSI acquisition inevitably results in the
blending of noise. The noise not only reduces visual
quality but also complicates data processing. Thus, HSI
denoising is a crucial step of HSI processing. Due to the
low-rank image and sparse noise structures of HSIs, lowrank
and SR (LSASR)-based methods are widely used for
HSI denoising.
MARCH 2022 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
DENOISING BASED ON SR
Assume that noise is additive. Then an observation model
can be expressed as
YX ,N=+
where Y yy yRM
= [, ,, ]f !
12
#
with L spectral bands and M pixels, X xx xRM
is the original clean HSI data, and N RLM
!
12
#
(1)
LM is the observed HSI data
= [, ,, ]f ! LM
#
is the noise.
Based on the assumption that the clean signal is a linear
combination of a few atoms in a dictionary while the noise
component is not, denoising can be explored as a sparse
signal recovery task. Given an SR model
XD ,A=
NOMENCLATURE
HS
HRHS
LRHS
HSI
SR
SRC
SRD
JSR
KJSR
LRR
TV
LRMR
RPCA
LRTR
GF-5
VNIR
SWIR
SNR
PAN
MS
LMM
NMF
COM
RKHS
SSC
SGDA
SVM
ASC
EMAP
CNN
CR
RBF
SOMP
SCI
LBP
LRMD
(2)
Hyperspectral
High-spatial-resolution HS
Low-spatial-resolution HS
Hyperspectral image
Sparse representation
SR-based classification
SR detector
Joint SR
Kernel-based JSR
Low-rank representation
Total variation
Low-rank matrix recovery
Robust principal component analysis
Low-rank tensor recovery
Gaofen-5
Visible and near infrared
Short-wave infrared
Signal-to-noise ratio
Panchromatic
Multispectral
Linear mixing model
Nonnegative matrix factorization
Constrained optimization model
Reproducing kernel Hilbert space
Sparse subspace clustering
Sparse graph-based discriminant analysis
Support vector machine
Abundances' sum-to-one constraint
Extended multiattribute profile
Convolutional neural network
Collaborative representation
Radial basis function
Simultaneous orthogonal matching pursuit
Sparsity concentration index
Local binary patterns
Low-rank matrix decomposition
11
IEEE Geoscience and Remote Sensing Magazine - March 2022

Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - March 2022
