IEEE Geoscience and Remote Sensing Magazine - March 2023 - 27

data processing: HS restoration, compressive sensing (CS),
anomaly detection (AD), HS-multispectral (MS) fusion,
and spectral unmixing (SU). For each topic, we elaborate
on the remarkable achievements of tensor decomposition
models for HS RS, with a pivotal description of the existing
methodologies and a representative exhibition of
experimental results. As a result, the remaining challenges
of the follow-up research directions are outlined and
discussed from the perspective of actual HS RS practices
and tensor decomposition merged with advanced priors
and even deep neural networks. This article summarizes
different tensor decomposition-based HS data processing
methods and categorizes them into different classes, from
simple adoptions to complex combinations with other
priors for algorithm beginners. We expect that this survey
provides new investigations and development trends for
experienced researchers to some extent.
INTRODUCTION
HS RS imaging has gradually become one of the most vital
achievements in the field of RS since the 1980s [1], [2].
Varied from an initial single-band panchromatic image, a
three-band red-green-blue (RGB) image, and a several-band
MS image, an HS image contains hundreds of narrow and
contiguous spectral bands, promoted by the development
of spectral imaging equipment and improvement of spectral
resolutions. The broader portion of the HS spectrum can
scan from the ultraviolet, extend into the visible spectrum,
and eventually reach the near infrared, or shortwave infrared
[3]. Each pixel of HS images corresponds to a spectral
signature and reflects the electromagnetic properties of the
observed object. This enables the identification and discrimination
of underlying objects, especially some that have similar
properties in single- and several-band RS images (such
as panchromatic, RGB, and MS) in a more accurate manner.
As a result, the wealth of spatial and spectral information in
HS images has extremely improved the perceptual ability of
Earth observation, which makes the HS RS technique play a
crucial role in fields such as precision agriculture (e.g., monitoring
the growth and health of crops), space exploration
(e.g., searching for signs of life on other planets), pollution
monitoring (e.g., the detection of ocean oil spills), and military
applications (e.g., the identification of military targets)
[4], [5], [6].
Over the past decade, massive efforts have been made
to process and analyze HS RS data after data acquisition.
Initial HS data processing considers either a gray-level
image for each band or the spectral signature of each
pixel. From one side, each HS spectral band is regarded
as a gray-level image, and traditional 2D image processing
algorithms are directly introduced band by band
[7], [8]. From another side, spectral signatures that have
similar visible properties (e.g., color and texture) can be
used to identify materials [9]. Furthermore, extensive
low-rank (LR) matrix-based methods are employed to
explore the high correlation of spectral channels, with
MARCH 2023 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
the assumption that the unfolding HS matrix has an
LR property [10], [11], [12]. Given an HS image of size
hv ,z## the recovery of an unfolding HS matrix ()
hv z#
usually requires singular value decomposition (SVD),
which leads to a computational cost of ()
Oh vz z3
22
+
[13], [14], [15]. In some typical tensor decompositionbased
methods, the complexity of the tensor SVD
(t-SVD) is about ()
Oh logvz zhvz2
+
[16], [17], [18]. Compared
to matrix forms, tensor decompositions achieve
excellent performance with a tolerable increment of
computational complexity.
However, these traditional
LR models reshape each
spectral band as a vector,
leading to the destruction of
the inherent spatial neighborhood
similarity and correlation
between the spatial
and spectral informat ion
of HS images. Correct interpretations
of HS images
and the appropriate choice
of intelligent models should
be determined to reduce the
gap between HS tasks and the advanced data processing
technique. Both 2D spatial information and 1D spectral
information are considered when an HS image is modeled
as a three-order tensor.
Tensor decomposition, which originates from Hitchcock's
work in 1927 [19], touches upon numerous disciplines,
but it has become significant in the fields of signal
processing, machine learning, data mining, and fusion
over the past 10 years [20], [21], [22]. Early overviews
focused on two common decomposition ways: Tucker
decomposition and canonical decomposition/parallel
factor analysis (CP) decomposition. In 2008, these two
decompositions were first introduced into HS restoration
tasks to remove Gaussian noise [23], [24]. Tensor decomposition-based
mathematical models avoid converting
the original dimensions and, to some degree, enhance
the interpretability and completeness of problem modeling.
Different types of prior knowledge (e.g., nonlocal
similarity in the spatial domain and spatial and spectral
smoothness) in HS RS are considered and incorporated
into tensor decomposition frameworks. However, on the
one hand, additional tensor decomposition methods
have been proposed recently, such as block term (BT)
decomposition, t-SVD [25], tensor train (TT) decomposition
[26], and tensor ring (TR) decomposition [27]. On
the other hand, as a versatile tool, tensor decomposition
related to HS image processing has not been reviewed.
In this article, we mainly present a systematic overview
from the perspective of state-of-the-art tensor decomposition
techniques for HS data processing in terms of the
five burgeoning topics previously mentioned, as presented
in Figure 1.
27
THE WEALTH OF SPATIAL
AND SPECTRAL
INFORMATION IN HS
IMAGES HAS EXTREMELY
IMPROVED THE
PERCEPTUAL ABILITY OF
EARTH OBSERVATION.
IEEE Geoscience and Remote Sensing Magazine - March 2023

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