IEEE Geoscience and Remote Sensing Magazine - March 2023 - 60

low-rankness regularization of abundances. The unmixing
results of LR-NTF are superior to those of other competitive
approaches on the urban data, demonstrating its superiority
and effectiveness.
FUTURE CHALLENGES
Several advanced tensor decomposition-based methods
have recently achieved effectiveness in HS SU. Nonetheless,
there is still a long way to go toward the definition of
statistical models and the design of algorithms. In the following,
we briefly summarize some aspects that deserve
further consideration.
The SU workflow usually contains the preprocessing
step of estimating the NOE, and it plays a crucial role in
the field of SU [235], [236]. However, almost all NOE approaches
convert HS data into 2D and perform matrixbased
estimation. Recent research in [134] demonstrates
the potential of tensor-based NOE methods in preventing
data loss. In this way, these methods based on tensor decomposition
can further be exploited to yield good performance
for NOE estimation, especially in scenes with high
mixing and outliers.
The most commonly utilized evaluation indices for HS
SU include the RMSE (which measures the error between
the estimated abundance map and reference abundance
map) and SAD (which assesses the similarity of the extracted
endmember signatures and true endmember signatures).
However, the RMSE and SAD contribute to a quantitative
comparison of SU results only when ground truth for
abundances and endmembers exists. If there are no references
in a real scenario, meaningful and suitable evaluation
metrics should be developed in future work.
Traditional NLMMs are readily interpreted as matrix
factorization problems. The tensor decomposition-based
NLMM has been springing up in recent years. We should
consider complex interactions, such as intimate and multilayered
mixture, for establishing general and robust tensor
models. In addition, the rise of deep learning techniques
provides unprecedented success for SU, owing to their
powerful learning ability [237], [238], [239], [240], [241],
[242], [243]. However, most deep learning-based unmixing
methods focus on the LMM, thereby resulting in detailed
information loss. The combination of deep learning and
tensor decomposition models can effectively ensure the
TABLE 12. A QUANTITATIVE COMPARISON OF DIFFERENT
METHODS FOR HS SU.
METHOD
SAD
Asphalt
Grass
Tree
Roof
MSAD
RMSE
60
MVNTF MVNTF-TV
0.3738
0.2572
0.1474
0.2825
0.2652
0.2638
0.2606
0.1722
0.145
0.2273
0.2013
0.2588
SeCoDe LR-NTF
0.1127
0.1349
0.219
0.045
0.0854 0.0632
0.3861 0.0395
0.1839 0.0876
0.1453 0.1451
spectral and spatial information of HS data, further yielding
significant unmixing performance improvement.
Another important challenge is the time consumption
of high-performance SU architectures, which hinders their
applicability in real scenarios. In particular, as the NOE
and size of an image increase, current NTF-based unmixing
methods have difficulty dealing with this situation, owing
to high computational consumption. Therefore, the exploration
of more computationally efficient tensor-based approaches
will be an urgent research direction in the future.
CONCLUSION
The HS technique accomplishes the acquisition, utilization,
and analysis of nearly continuous spectral bands and
permeates a broad range of practical applications, having
attracted increasing attention from researchers worldwide.
In HS data processing, large-scale and high-order properties
are often involved in collected data. The ever-growing
volume of 3D HS data puts higher demands on processing
algorithms to replace 2D matrix-based methods. Tensor
decomposition plays a crucial role in both problem modeling
and methodological approaches, making it possible
to leverage the spectral information of each complete 1D
spectral signature and spatial structure of each complete 2D
spatial image. In this article, we presented a comprehensive
and technical review of five representative HS topics,
including HS restoration, CS, AD, HS-MS fusion, and SU.
Among these, we reviewed current tensor decompositionbased
methods, with main formulations, experimental illustrations,
and remaining challenges. The most important
and compatible challenges related to consolidating tensor
decomposition techniques for HS data processing should be
emphasized and summarized in five aspects: model applicability,
parameter adjustment, computational efficiency,
methodological feasibility, and multimission applications:
1) Model applicability: Tensor decomposition theory and
practice offer us versatile and potent weapons to solve
various HS image processing problems. A high-dimensional
tensor is often decomposed by different categories
of tensor decomposition into several decomposition
factors/cores. One sign reveals that the mathematical
meaning of different factors/cores should be made in
connection with the physical properties of the HS structure.
Another sign is that each HS task contains multiple
modeling problems, such as various types of HS noise
(i.e., Gaussian noise, stripes, and mixed noise) caused by
different kinds of sensors and external conditions. Tensor
decomposition-based models should be capable of
characterizing specific HS properties and use in different
scenarios. Beginners and experienced practitioners
are expected to learn basic knowledge of tensor decompositions
from tutorials and references [20], [22], [25],
which contribute to building readers' awareness of tensorial
theory. We also recommend several materials and
references related to HS RS applications to master the
imaging properties and image features, including the
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