IEEE Geoscience and Remote Sensing Magazine - March 2023 - 50

find a more appropriate tensor decomposition for HS CS is
a vital challenge.
Noise degradation usually has a negative influence
on HS CS sampling and reconstruction, which is hardly
ignored in the real HS CS real imaging process. As a
result, considering the noise interference and enhancing
the robustness of noise in the CS process remain
challenging.
HYPERSPECTRAL ANOMALY DETECTION
HS AD aims to discover and separate potential man-made
objects from observed image scenes, which is typically constructive
for defense and surveillance developments in RS
fields, such as mine exploration and military reconnaissance.
Anomalies can be a pixel, a set of pixels, a feature,
and a series of features. They rarely occur in HS images,
and their spectral signatures differ from the surrounding
background environment. For instance, unknown aircraft
and vehicles suddenly appear in a suburb or bridge scene,
usually marked as anomalies. In Figure 18, AD can be regarded
as an unsupervised two-class classification problem
where anomalies occupy small areas compared with their
surrounding background. The key to coping with this problem
is to exploit the discrepancy between anomalies and
their background. Anomalies commonly occur with low
probabilities, and their spectral signatures are quite different
from their neighbors.
HS images containing two spatial dimensions and one
spectral dimension are intrinsically considered a three-order
tensor. Tensor-based approaches have been gradually gaining
attention in HS AD in recent years. Tucker decomposition is
the first and essential type of tensor decomposition method
used for HS AD. Therefore, in the following sections, we
mainly focus on Tucker decomposition-based methods and
a few other types of tensor-based methods.
TENSOR DECOMPOSITION-BASED HYPERSPECTRAL
ANOMALY DETECTION METHODS
TUCKER DECOMPOSITION-BASED METHODS
An observed HS image T can be decomposed into two
parts by Tucker decomposition; i.e.,
TX S=+
(49)
where X is an LR background tensor and S is a sparse tensor
consisting of anomalies. The Tucker decomposition for
AD is formulated as the following optimization:
'
ST X
X
==
A
BB B
## #
11 22 33
.
(50)
Many Tucker decomposition-based variants have been
studied to improve AD accuracy. Li et al. [70] proposed an
4,500
4,000
3,500
3,000
2,500
2,000
1,500
1,000
500
050 100 150 200
Band Number
+
Background
FIGURE 18. HS image anomaly detection.
50
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE MARCH 2023
Anomalies
Reflectance

IEEE Geoscience and Remote Sensing Magazine - March 2023

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