IEEE Geoscience and Remote Sensing Magazine - June 2013 - 24

vectors that have significant spectral differences from their
surrounding background pixels. Man-made anomalies can
also be detected through change detectors [125], [126],
which are used to identify changes within a scene that
occur over time. The second stage is to identify whether or
not the anomaly is a target or natural clutter. This stage can
be achieved if the spectral signature of the target is known
which can be obtained from a spectral library [122] or from
a set of training data which could also be synthetically generated [127]. Almost all the classical target detection techniques in the literature [127]-[131] are based on a linear
process that only exploits the first and second order statistics to identify anomalies or targets. Advanced nonlinear
detection techniques based on statistical kernel learning
theory [132] have also been developed in [133] that indirectly exploit the higher order statistics between the spectral bands through a kernel function [132].
A. AnoMAly Detection
Anomaly detectors, outlier detectors, or novelty detectors are pattern recognition or statistical schemes that are
used to detect objects that stand out from their cluttered
background. In spectral anomaly detection algorithms
[123], [124], [134]-[136] pixels (materials) that have a significantly different spectral signature from their neighboring background clutter pixels are identified as spectral
anomalies. In such algorithms, no prior knowledge of the
target spectral signature is utilized or assumed. In [134], a
spectral anomaly detection algorithm was developed for
detecting targets of unknown spectral distribution against
a background with unknown spectral covariance. This
algorithm is now commonly referred to as the Reed-Xiaoli
(RX) anomaly detector, has been successfully applied to
many hyperspectral target detection applications [7], [124],
[135], [136] and is considered as the benchmark anomaly
detection algorithm for multispectral/hyperspectral data.
The RX algorithm is a constant false alarm rate adaptive
anomaly detector which is derived from the generalized
likelihood ratio test (GLRT). Assuming a single pixel target
y as the observation test vector, the results of RX-algorithm
is given by
t b-1 (y - nt b),
RX (y) = (y - nt b) T C

19
9
7
19

Inner Window
Region (IWR)

9 7

Current Test
Pixel
Outer Window
Region (OWR)

Guard (Band)
Window

FIGURE 12. An example of a dual window.

24

(5)

where nt b is the estimated background clutter sample mean
t b is the estimated background clutter covariance.
and C
The background mean and covariance matrix can be
estimated globally from the whole hyperspectral image or
locally using a double concentric window approach [123].
t b globally the background pixels are usually
To estimate C
modeled as a mixture of multivariate Gaussian distributions [137], linear subspace [138], [139], linear or stochastic
mixture models [140] or by some clustering or segmentation
techniques [141]-[143] which are used to segment the background into several clusters. On the other hand the local
background covariance matrix can be estimated by using a
sliding double concentric window, centered at each test pixel,
which consists of a small inner window region (IWR) centered within a larger outer window region (OWR), as shown
in Fig. 12. The local background mean vector and covariance
matrix are then computed from the spectral pixels falling
within the OWR. The size of the inner window is assumed
to be the size of the typical target of interest in the image. A
guard band surrounding the IWR is also sometimes used
to prevent the target pixels from corrupting the calculation
of the background OWR statistics. The whole background
probability density function has also been modeled by a single class support vector machine in [144] and spectral pixels
that fall outside this model are considered as anomalies.
Anomaly detection techniques formulated as eliminating
the whole or local background subspace from every pixel
have also been investigated in [145].
Several variations of the RX detector that attempt to
alleviate the limitation of RX have been proposed in the literature [135]-[137]. In [146], a modification to the RX algorithm called SubSpace RX (SSRX) was outlined that is based
on the PCA of the background covariance matrix. In the
SSRX algorithm, several high-variance background dimensions are deleted before applying the RX algorithm as these
are assumed to capture non-normal background clutter variance. Another consideration in RX implementation is potential ill-conditioning of the local covariance matrix due to the
high correlation, high dimensionality of the hyperspectral
data and a limited background sample size. This ill-conditioning is typically addressed by a regularization procedure
such as PCA-based regularization or adding a scaled identity
matrix to the background covariance matrix [147].
B. signAtuRe-BAseD tARget Detection
In some applications, we have some prior knowledge about
the spectral characteristics of the desired targets. In these
situations, the target spectral characteristics can be defined
by a single target spectrum [148] or by a signal subspace
[129]. The GLRT detector using a single targets spectrum
is referred to as the spectral matched filter (SMF) and the
maximum likelihood abundance estimate of the target in a
test pixel y is given in [130] as
D SMF (y) =

t -1 y
sT C
T t -1 ,
s C s

ieee Geoscience and remote sensinG maGazine

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june 2013



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