IEEE Geoscience and Remote Sensing Magazine - March 2022 - 76

f zW is a decoder function with parameter
,( ,, ) is an encoder function with parameters
We and H, z) is the optimal z sought for x, and m and b
dd
e
z ,) and W ,e H, and Wd
are
where (, )
Wxf WHde
are regularization parameters. In the solution, the other
variables are first fixed to find
solved by iteration. Finally, the residual between x and xu
can be written as
r ()
u
xx x 2
f
===xz
W
xxWH W
2
ff
dd
de dd
(, )
(( ,, ), ).
2
(10)
Based on this, anomaly detection methods founded
on stack AEs have been proposed, in which testing pixel
x is encoded as z by a multilayer encoder [91], [93]. In addition,
to simultaneously utilize spectral and spatial information,
[98] adopts manifold learning to extract local
spatial structure information and integrates it with an AE
learning model. In [92], LRaSMD is used to divide the
original data into sparse and low-rank matrices, and a
stack self-coded network is adopted to study spatial and
spectral features, respectively.
Generally, existing GAN-based anomaly detection methods
combine AEs and GANs to form an adversarial generation
network (AAE), which adds a discriminator on the
basis of an AE. As detailed in Figure 8, a discriminator can
be added to code z [94], [95], [97] and to reconstruct xu
[96], [97], [99], depending on requirements. The role of a
discriminator is to determine whether the generated data
meet real needs, further guiding the generator (the encoder
for z or )xu
to produce better information to fool the discriminator.
Assuming that z is expected to obey a Gaussian
TABLE 2. A TAXONOMY OF PERFORMANCE EVALUATION
METHODS FOR HYPERSPECTRAL ANOMALY DETECTION.
CATEGORY CHARACTERISTICS
ROC and
AUC
The ROC describes the relationship
between the x-axis FPR and y-axis TPR
under different thresholds. The closer
the curve is to the upper-left corner
of the coordinate axis, the better the
performance is. The AUC is the area
under the ROC, which can quantitatively
describe accuracy of an algorithm.
Box plot
The box plot can intuitively reflect the
anomaly-background separability. The
bigger the gap between the abnormal
box and the background box, the higher
the anomaly-background separation
will be. The shorter the background
box, the more background information
can be effectively suppressed.
SER and
AER
The SER and AER can accurately evaluate
the performance of algorithms, while
the ROC cannot. The smaller the value
of the SER and the larger the value of
AER, the better the detection will be.
FPR: false positive rate; TPR: true positive rate.
76
REPRESENTATIVE
REFERENCE
The ROC [124]
and some
description of
the ROC for
AD [66]
distribution, the z output by the generator and the sampled
z from the Gaussian distribution are input into the discriminator
to guide the generator to produce a z that obeys
the Gaussian distribution. Therefore, an AAE includes two
stages: a reconstruction period of testing pixels to obtain
the minimum error and a regularization constraint phase,
alternately updating the discriminant and generating networks
to improve the ability of the generator (the encoder
or decoder). Obviously, an AAE network uses only the
spectral information of images. Moreover, anomaly detection
through deep learning networks is poor, so many approaches
also mine the spatial information of images for
better results [92], [98], [99].
REAL-TIME ANOMALY DETECTION METHODS
Advanced unmanned aerial vehicle technology has enabled
data acquisition to break through temporal and
spatial resolution limitations [118] and greatly increased
hyperspectral imaging's applications in environmental monitoring,
national defense surveillance, and precision agriculture.
Real-time processing for airborne data becomes
the primary requirement in support of immediate decision
making. The classical RX algorithm real-time computation
problem has been studied. Since most hyperspectral
sensors perform push broom scanning imaging, updating
sample correlation and covariance matrices is usually carried
out line by line [118], [119], such as through real-time
recursive causality [100], [101], streaming background statistics
[102], and so on, which do not take advantage of
future image information. In the matrix inverse adaptive
calculation [120]-[123], optimization [101], [103], [119]
and Cholesky decomposition [101] can effectively shorten
running times. In addition, the parallel computing version
of the RX algorithm is mainly studied on GPUs [104] and
multicore platforms [103], and some research shows obvious
GPU acceleration [105]. In terms of hardware design,
based on the constrained energy minimization algorithm
in target detection and the RX algorithm in anomaly location,
a two-module field-programmable gate array (FPGA)
is designed [102] that can transform the necessary methods
according to requirements.
Box plot [125]
and some
description of
the box plot for
AD [42], [126]
PERFORMANCE EVALUATION METHODS
FOR ANOMALY DETECTION
To assess detection performance, this article investigates
the following five metrics: the receiver operating characteristic
(ROC) curve and area under the ROC curve (AUC),
box plot, and square error ratio (SER) and area error ratio
(AER), as summarized in Table 2.
The SER, AER,
and actual
applications
[127], [128]
RECEIVER OPERATING CHARACTERISTIC AND
AREA UNDER THE RECEIVER OPERATING
CHARACTERISTIC CURVES
The ROC curve is a classic index for evaluating detection
performance. It describes the relationship between detection
rate PD
and false alarm rate P .FA When a specific
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE MARCH 2022
IEEE Geoscience and Remote Sensing Magazine - March 2022

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