IEEE Geoscience and Remote Sensing Magazine - June 2019 - 95

x = cs + v,

(44)

where v characterizes the clutter of (39) and corresponds
with (31) and (33). Because c can be positive or negative,
the hypotheses we wish to choose from are
H 0 : c = 0 Gas absent,

(45)

H 1 : c ! 0 Gas present.

(46)

There are two families of algorithms used in gas detection applications depending on the sensor configuration.
IMAGING SPECTROMETERS
Changing the two hypotheses from the MF and NMF of
(37) and (38), respectively, can produce positive or negative values depending on c, but a detection is declared only
when the score y exceeds some threshold, which ignores the
output when c is negative. One solution is to square the
detectors, yielding a set of algorithms appropriate for gas
detection. The MF and NMF become the squared matched
filter (MF2) and the squared normalized matched filter
(NMF2) and are written as
y MF2 =
y NMF2 =

(s T C b-1 x) 2
= y 2MF,
s T C b-1 s

(47)

(s T C -b 1 x) 2
= y 2NMF,
(s C -b 1 s)(x T C -b 1 x)

(48)

where x is the at-aperture radiance and s is the band-averaged library signature for the chemical of interest. The price
paid for squaring the detection statistic is a higher false
alarm rate for a given detection level. Typically, the covariance matrix is estimated from background data. For imaging sensors, when the chemicals of interest are rare, the
estimation procedure is relatively simple; when the plume
is strong or takes up a large portion of the image, however,
self-cancellation of the target signal is possible.
Comparing the detection algorithms to the signal model of (40), there are several reasons that the detection of
gases is nontrivial. The algorithm uses the library signature,
band-averaged to the wavelengths of the sensor, and operates on the principle that the signal varies linearly with the
signature. However, the signal contributed by the plume is
corrupted by the atmosphere, the background, the thermal
contrast term, and the nonlinearity of Beer's law. These effects lead to mismatch between the observed signal added
by the plume and the library spectrum. Having a good
model for the background and atmosphere is key to having a low false alarm rate. If the plume is very thick along
the viewing path, Beer's law can make the plume opaque
and cause the measured spectrum to be drastically different from the library spectrum and even cause it to look like
other chemicals in the library. In the thick-plume situation,
the linear algorithms described here are not ideal.
There is a tradeoff involved with the thermal contrast
term, especially for side-looking sensors. The larger the
JUNE 2019

IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

thermal contrast, the larger the signal from the plume will
be. If the plume is in equilibrium with the atmosphere, then,
near the ground, the temperature contrast may be relatively small, but the background radiance will not have many
atmospheric features. Low thermal contrast means poor
signal levels, but the lack of atmospheric features means a
better match between the signature and the measurement,
and, because it is easier to model the background radiance,
algorithms can be designed to have low false alarm rates. If
a side-looking sensor views the plume in front of a cold sky,
then there can be a large thermal contrast, but the measured
radiance will contain many atmospheric features. Modeling
the background radiance in this case is more difficult and
can lead to false alarms. Understanding how to design algorithms for both situations is an important aspect for future
standoff sensor applications.
The techniques mentioned up to this point have been
in the radiance domain and are generally applicable to
imaging sensors. Imaging detection techniques have
also been applied to the Airborne Visible InfraRed Imaging Spectrometer-Next Generation data for methane
detection [101]. Another technique for airborne sensors
actually performs AC and TES to find the emissivity of
each pixel and then uses the detection algorithms described here on the emissivity spectra. Emissivity-based
techniques have recently been used for the detection
and mapping of methane leaks [102] and other chemical
emissions [28], [103]. The key observation here is that
canceling out atmospheric effects for common chemicals
like water vapor and carbon dioxide will leave the effects
of rare chemicals.
NONIMAGING ("SINGLE-PIXEL") SPECTROMETERS
For standoff applications where the sensor is persistently
monitoring an area or is vehicle mounted, single-pixel
spectrometers are typically used instead of imaging spectrometers [100]. Single-pixel sensors acquire fewer spectra
than imagers, which makes it difficult to estimate the statistical variability of the background clutter and use the detection algorithms described earlier. Algorithms designed
for single-pixel sensors produce a detection result for each
spectrum individually but do not use "background" measurements in the detection process. As with imaging algorithms, one of the major challenges in single-pixel methods
is to adequately suppress background clutter while detecting the signal of interest.
Regression and "structured background" techniques differ from the previous algorithms because the background
variation is incorporated into the model without estimation from the data. The basic idea is to fit models to each
spectrum and then decide which model fits best. Each
model incorporates known background spectra and library
chemical spectra. There are several different methods available; see [104] for a summary.
A simple detection pipeline for single-pixels sensors is
shown in Figure 17. The process works as follows.
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IEEE Geoscience and Remote Sensing Magazine - June 2019

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