IEEE Geoscience and Remote Sensing Magazine - June 2019 - 92

to LWIR data and allow for improvements to existing processing techniques.
CHALLENGES
The main difficulties in successfully modeling and classifying background materials are 1) a lack of comprehensive
ground truth for training or testing of results, 2) the immaturity of upstream processing and hardware, and 3) the lack
of spectral separation between different materials. A lack
of ground-truthed data prevents different algorithms or
results from being compared. Uncertainty in the retrieved
emissivity makes it difficult to successfully classify different materials. This problem is compounded by materials
having little statistical separation between them. The development of comprehensive models for the temperature
and emissivity variation in LWIR backgrounds is an area of
ongoing development that would be highly beneficial for
assessing and improving processing algorithms.
SOLID-PHASE TARGET DETECTION
The development of detection algorithms for solid targets
using VNIR-SWIR HSI sensors has reached a mature state
[86]. These algorithms use reflectance target libraries and
operate on reflectance data cubes. The same algorithms
can be used for detection in the LWIR region; however,
differences in signal phenomenology are expected to affect implementation and performance in the LWIR region.
Matched filter-(MF)-type algorithms [1], [87], which have

been proven extremely effective in the reflective spectral
region [88], [89], are strong candidates for use in the LWIR
emissivity domain.
Detection algorithms for radar and communications
applications use the additive signal model
x = as + v,

where a is a constant, s is the signature of the target, and
v represents the combined effects of background clutter
and sensor noise. In contrast, solid-phase or hard targets
are better represented by the replacement target model [1]
(32)

x = as + (1 - a) v, 0 # a # 1,

where a is the target fill fraction. Deriving practical detection algorithms for this constrained model is quite challenging. However, as has been demonstrated in [1] and [86],
we can bypass this obstacle using a geometrical viewpoint.
To this end, suppose that we observe the vector x, generated by a multivariate Gaussian distribution with mean as
and covariance matrix C b, i.e.,
(33)

x~N (as, C b),

and we wish to choose one of the following hypotheses:
(34)
(35)

H 0 : a = 0,
H 1 : a 2 0.

Whitened Space

Measurement Space
x2

(31)

x~2

H1: x ∼ N (as, Cb)

Target NMF
~
as

False Alarms

as

~
x

x
~
x = Cb-1/2x
a>0

θ

Whitening

yMF

Target MF
Detections

0
H0: x ∼ N (0, Cb)

x~1

0

x1
Target Anomaly Detector

Anomaly Detector

MF

~
yAD = ixi2

~
~
sT x
yMF = ~
isi

Omnidirectional Search

Hyperplanar Search

Decision Boundaries
NMF
yNMF =

~
~
sT x
~
~ = cos θ
isi ixi

Hyperconical Search

FIGURE 15. The decision surfaces and mathematical formulas of an anomaly detector, an MF, and an NMF in the whitened space for the
common covariance Gauss-Gauss detection problem.

92

IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

JUNE 2019
IEEE Geoscience and Remote Sensing Magazine - June 2019

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