Background Radiance Estimation for Gas Plume Quantification for Airborne Hyperspectral Thermal Imaging

Abstract

Hyperspectral imaging in the long-wave infrared (LWIR) is a mean that is proving its worth in the characterization of gaseous effluent. Indeed the spectral and spatial resolution of acquisition instruments is steadily decreasing, making the gases characterization increasingly easy in the LWIR domain. The majority of literature algorithms exploit the plume contribution to the radiance corresponding to the difference of radiance between the plume-present and plume-absent pixels. Nevertheless, the off-plume radiance is unobservable using a single image. In this paper, we propose a new method to retrieve trace gas concentration from airborne infrared hyperspectral data. More particularly the outlined method improves the existing background radiance estimation approach to deal with heterogeneous scenes corresponding to industrial scenes. It consists in performing a classification of the scene and then applying a principal components analysis based method to estimate the background radiance on each cluster stemming from the classification. In order to determine the contribution of the classification to the background radiance estimation, we compared the two approaches on synthetic data and Telops Fourier Transform Spectrometer (FTS) Imaging Hyper-Cam LW airborne acquisition above ethylene release. We finally show ethylene retrieved concentration map and estimate flow rate of the ethylene release.

Full text

Research Article
Background Radiance Estimation for Gas Plume Quantification
for Airborne Hyperspectral Thermal Imaging
Ramzi Idoughi,1,2 Thomas H. G. Vidal,1Pierre-Yves Foucher,1
Marc-André Gagnon,3and Xavier Briottet1
1ONERA, e French Aerospace Lab, DOTA, 2 Avenue Edouard Belin, 31400 Toulouse, France
2Institut Sup´
erieur de l’A´
eronautiqueetdel’Espace(ISAE),Toulouse,France
3Telops Inc., 100-2600 St-Jean-Baptiste Avenue, Qu´
ebec, QC, Canada G2E 6J5
Correspondence should be addressed to Pierre-Yves Foucher; pierre-yves.foucher@onera.fr
Received  October ; Accepted  February 
Academic Editor: Hassen Aroui
Copyright ©  Ramzi Idoughi et al. is is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Hyperspectral imaging in the long-wave infrared (LWIR) is a mean that is proving its worth in the characterization of
gaseous euent. Indeed the spectral and spatial resolution of acquisition instruments is steadily decreasing, making the gases
characterization increasingly easy in the LWIR domain. e majority of literature algorithms exploit the plume contribution to the
radiance corresponding to the dierence of radiance between the plume-present and plume-absent pixels. Nevertheless, the o-
plume radiance is unobservable using a single image. In this paper, we propose a new method to retrieve trace gas concentration
from airborne infrared hyperspectral data. More particularly the outlined method improves the existing background radiance
estimation approach to deal with heterogeneous scenes corresponding to industrial scenes. It consists in performing a classication
of the scene and then applying a principal components analysis based method to estimate the background radiance on each cluster
stemming from the classication. In order todeter mine the contribution of the classication to the background radiance estimation,
we compared the two approaches on synthetic data and Telops Fourier Transform Spectrometer (FTS) Imaging Hyper-Cam LW
airborne acquisition above ethylene release. We nally show ethylene retrieved concentration map and estimate ow rate of the
ethylene release.
1. Introduction
Anthropogenic sources, especially industrial, have a major
contribution to air pollution and security issues. However,
these emissions remain poorly estimated at a high spatial
resolution over heterogeneous scenes, like industrial plants.
Most of these emissions present a spectral signature
in the thermal infrared domain. is is the reason why
thermal hyperspectral imaging systems are deployed for their
characterization. More, as such plume has a small extent
they require a high spatial resolution imagery which can be
achieved with existing airborne systems [–].
However, signature of gaseous euents diers highly
fromusualtargetssincetheplumemodiesthespectral
signature of the background: dierent pixels in the data cube
that contain the same gaseous plume could have a totally
dierent spectral signature. At rst order, spectral signature
of these pixels will correspond to background spectra aected
by either absorption or emission of the gas. is variability
depends on background materials and temperature dierence
between the ground and the plume.
Existing approaches which use the spectral information
of such sensor to characterize gas plume can be divided
into two stages: endmember decomposition techniques to
estimate the background properties [–] and trace element
detection [–] or quantication methods [–] based on
estimated gas dierential signature (dierence for each “on-
plume pixel” between measured radiance and “o-plume”
estimated radiance). en it has been shown that background
uncertainty and heterogeneity are one of the major sources
of incertitude in gas quantication and detection limit [–
]. Depending on the ground properties the same amount
Hindawi Publishing Corporation
Journal of Spectroscopy
Volume 2016, Article ID 5428762, 17 pages
http://dx.doi.org/10.1155/2016/5428762

Journal of Spectroscopy
of gas can have a signature; thus a retrieved concentration is
modied by a factor of ten.
is paper aims to reduce the quantication error due to
misestimation of background properties.
To deal with ground variability for heterogeneous scene,
clustering was suggested to compute covariance matrices of
dierent spatial classes composing the background [, ],
thus creating independent classes on which detection algo-
rithms are applied.
e major limitation of these methods is that clustering
background step may be contaminated by the presence of the
gas plume [, , ].
If existing in the reective domain, for example, the very
weak gas plume signature has little impact on the clustering
stage [, ]. But for quite strong signature in the thermal
domain, gases plume anomalous classes can appear.
To overcome such issues, the clustering phase should be
achieved outside the spectral bands corresponding to the
strong absorption of the gas to be detected. Some recent
works [] show that such Selected-Band approach can be
used to estimate background radiance under the plume with
an interesting precision for various scenes.
In this paper, we look for a background estimation
method that will eciently reduce the gas retrieval quanti-
cation error in the case of heterogeneous scene. In this work
weintroduceanovelmethodtoestimatepixelbypixeltheo-
plumeradianceundertheplumeandthespecicadditional
spectral signature introduced by the gas plume using airborne
hyperspectral data.
is method aims to overcome the diculties that arise
from the inherent mixture of the heterogeneous background
and the gas plume spectra. We decompose the scene accord-
ing to the spectral-spatial information, and, for each pixel of
each cluster, we estimate dierential gas signature taking into
account background variability and gas spectral behavior.
is paper is structured as follows. Section  is dedicated
to the description of the methodology. en, Sections 
andevaluatetheapplicationofourmethodonsynthetic
data and Telops Hyper-Cam airborne platform data. Finally,
concluding remarks are given in Section .
2. Methodology
2.1. Plume Detection. Plume detection is an important step
for gas quantication process. It allows selecting the plume
area, where the background radiance has to be estimated, and
the o-plume area useful to getting background properties.
In the literature, several algorithms have been proposed
to detect the presence of gas from hyperspectral data. Spectral
Matched Filter (SMF) [] was chosen in this study because it
produced a good detection of the plume with a low number
of false alarms.
Let Xbe a hyperspectral image of pixels and Bbands,
represented by an ×Bmatrix. With Tbeing the gaseous
targetspectrum,wecanwritefortheth pixel x𝑖of the
hyperspectral image X:
x𝑖=T⋅𝛼𝑖+d,()
where 𝛼is the target t coecients (abundances) and dis the
residual vector to be minimized. To retrieve the abundances
𝛼,weneedtosolvetheunconstrainedregression(see()).e
analytic solution of this regression is
𝛼𝑖=T𝑇Σ−1
Xx𝑖
T𝑇Σ−1
XT,()
where ΣXisthecovariancematrixofthisscene.Anunbiased
estimation of ΣXcan be calculated as follows:
ΣX=1
−1⋅𝑁

𝑖=1 x𝑖−xx𝑖−x𝑇.()
We consider here the targeted gases as known. Hence, we
usethespectraoftargetedgasesfromthePacicNorthwest
National Laboratory (PNNL) absorbance Library [, ] to
construct T. e detection performance can be improved by
using an estimation of ΣXinvolving only plume-absent pixels.
Once the vector of abundances 𝛼is calculated, the plume
mask is deduced by thresholding.
2.2. Selected-Band Approach (SB). e principal components
analysis (PCA) was applied by many authors [, , ] in
order to obtain a representation of the background radiance
of plume-present pixels (bkg()). First, the principal vectors
are computed using the plume-absent pixels radiances. en,
background radiances of plume-present pixels are assumed
to lie in the subspace spanned by these principal vectors.
Niu et al. [] go even further by developing an approach
to estimate the background radiance. is approach is based
onthefactthat,inplumepresence,theon-plumeradiance
(on()) is essentially equal to its background (o-plume)
radiance over the most transparent spectral bands. Using
this observation, they combine a Selected-Band algorithm to
determine these transparent spectral bands with the PCA in
order to estimate bkg.
ereaer, in the present paper, we shall refer to this
method simply as Selected-Band (SB).
Aer a plume detection on the hyperspectral image X,
o pixels do not contain any plume gas. A o ×Bmatrix
Lo isconstructedbyarrangingtheo-plumemeasured
radiance spectra. A PCA model is then given by
Lo =Uo ⋅PT+Eo ,()
where Uo is an o ×pmatrix of coecients for plume-
absent pixels, Pis an B×pof principal components, and
Eo is the residual matrix. pisthenumberofconsidered
principal components. For the used data, we found p=10
to be an appropriate choice. It allows us to save more than
99.9% of the information.
Since the background radiances of plume-present pixels
areassumedtolieinthesubspacespannedbytheprincipal
components P,thematrixLbkg of the background radiance
spectra of the on plume-present pixels could be expressed
as follows:
Lbkg =U⋅PT+Ebkg.()

Journal of Spectroscopy 
Uis an on ×pmatrix of unknown coecients to be deter-
mined. Ebkg istheresidualmatrixinthiscase.
For this purpose, a second PCA model is written for the
on plume-present pixels, using only the SB bands, where
the gas absorption coecient is virtually nil:
Lsb
bkg =Lsb
on =U⋅PsbT+Eon,()
where Lsb
on is an on ×SB matrix, containing the on-plume
measured radiance spectra for the selected bands. PsbT
is an
SB ×pmatrix of principal components; Eon is the residual
matrix.
By using the Moore-Penrose pseudoinverse of the matrix
Psb (Psb†=(PTP)−1PT), a least-square estimate for Uis given
by
U=Lsb
on ⋅Psb†T.()
An estimation of the background radiances of plume-present
pixels is thus obtained by the following expression:
Lbkg =Lsb
on ⋅Psb†T⋅PT.()
e SB method has two leading limitations: the rst
comes from the assumption that Lsb
bkg =Lsb
on. is equality is
not eective if the temperature of the plume is dierent from
the ambient atmospheric temperature. Indeed, this temper-
ature dierence will have an impact on the transmission of
atmospheric gases and therefore on the on-plume radiance
outside gases signatures.
e second limitation relates to the case of heterogeneous
soil. SB method as presented by Niu et al. can be limited if
some background plume-present pixels are not well repre-
sented in plume-absent pixels. We propose otherwise to solve
this second point using a classication of the scene.
2.3. Clustering-Based Selected-Band Method (CSB Method)
2.3.1. Classication of the Scene. Since Funk et al. [] the
classication of a hyperspectral scene is a main preliminary
step of plume characterization through this scene. Funk et
al. showed that classication improves the results of plume
detection algorithms. ey concluded that clustering data
and removing the mean values could be seen as a type of
automatic background suppression.
Moreover, the classication of the scene aims to carry
o the disturbances on plume’s quantication due to the
heterogeneity of the soil [].
In this subsection, we explain the classication process
in order to enhance the background radiance estimation. A
rst classication is carried out on the plume-present pixels
(a plume detection algorithm is executed upstream); another
is done on the rest of the image.
isclassicationsisorganizedintwostages:rst,weper-
form a principal components transform [] on the radiance
spectra of the pixels of interest. en, we just select the rst
components for further classication because the important
background information is included in these components.
Finally, we carry out a classical -means on these components
to classify the scene.
e interest of this dimension reduction is to shorten
the time processing of the -means algorithm, without
deteriorating its performances. e number of the retained
components depends on the image to be treated. Usually, the
use of the  rst principal components is sucient to have a
good classication of the scene.
We choos e t h e -means algorithm for our classication,
atonehand,becauseitisanunsupervisedalgorithm.us,it
will be appropriate for a large number of dierent hyperspec-
tral images. On the other hand, this algorithm is one of the
fastest clustering algorithms.
At the end of this step, we obtain Cclasses in the
area without plume and CP classes containing plume. e
number of these clusters depends on the threshold max,used
to specify the maximum distance of a pixel to the centroid of
its cluster.
2.3.2. Clustering-Based (CB) Background Radiance Estima-
tion. A rst approach of Clustering-Based (CB) background
radiance estimation we used consists in a classes matching
between the plume-present and plume-absent regions.
e area under the plume has a petty spatial extent
compared to the rest of the scene, whereof it only contains
a small number of classes. In most cases it stands to reason
to assume the classes under the plume as an extension of
classes outside the plume and we assume that the presence
of gas does not change the main properties of background.
Indeed, the threshold max is selected such that pixels belong-
ing to the same class have nearly the same characteristics
(ground temperature and emissivity, atmospheric proles).
us, within a class, the o-plume radiance o is very close
from one pixel to another.
For each plume-present class CP𝑖,theaveragespectrum
ofitspixelsiscalculated;itisthencomparedtotheaverage
spectra of all plume-absent classes (C𝑗)1≤𝑗≤𝑁C. Readers will
note that the comparison is performed only on bands where
the target gases absorption coecients are very small. Class
C𝑗∗ with the minimal distance from the plume-present class
CP𝑖and the latter are considered to be the same. For a pixel
xpin this class CP𝑖, we consider that its background radiance
bkg(xp)is equal to the mean radiance of pixels belonging to
class C𝑗∗.
e CB method bypasses the soil heterogeneity limitation
of the method SB. However, it does not take into account
the intraclass variability of the background radiance. In the
following paragraph we will present another Clustering-
Based method that appropriates the benets of SB and CB
methods of bkg estimation, without their shortcomings.
2.3.3. Clustering-Based Selected-Band Method (CSB Method).
In order to improve the background radiance estimation
given by the Selected-Band approach (see Section .) and
the Clustering-Based method (see Section ..), we propose
to perform this method on each cluster stemming from the
classication (Section ..).

Journal of Spectroscopy
Aer a plume detection, classications of the scene are
realized separately for plume-absent pixels and for plume-
present pixels; then each class of plume-present pixels is
associated with a plume-absent pixels class. For each plume-
present class CP𝑖, the Selected-Band approach is performed
using () with a matrix PT
C𝑗∗ derived from a PCA involving
the pixels of the class C𝑗∗. Recall that the latter corresponds
to the plume-absent class with the minimal distance from the
plume-present class CP𝑖:
LCP𝑖
bkg =Lsb CP𝑖
on ⋅Psb†T
CP𝑖⋅PT
CP𝑖.()
In the following sections, we will present the improve-
ment of background radiance estimation for plume-present
pixelsduetothisnewmethod,bothonsyntheticandreal
scenes.
3. Application on Synthetic Data
3.1. Presentation of the Synthetic Data. To eva l u a t e t h e p e r-
formances of background radiance estimation, synthetic data
of an industrial scene were used. ese data were simulated
using a tool we have developed in order to provide a
comprehensive test where the “truth” is known.
e dimensions of the simulated images are 200 ×
200×107(rows by columns by spectral dimension). e
wavenumber range used is 800to 1330cm−1 with a resolution
of 5cm−1. In this subsection, we describe the process of
synthetic data generation.
3.1.1. Ground Simulation. We rst dened the distribution
of soil composition. Several materials frequently present in
industrial scenes (asphalt, copper, aluminum, grass, etc.) were
chosen (see Figure ). en we attributed for each pixel of
the image the appropriate physical properties (emissivity and
temperature), according to the present material.
e emissivities were taken from ASTER data base
[]. Figure (b) represents the emissivities of the dierent
materials present through the synthetic scene.
e ground temperature varies widely depending on
weather conditions, soil composition, orientation of the sur-
faces, and the relief of the scene (shadow eect). It is therefore
verydiculttohavearealisticestimateofthisquantity.e
values we have chosen are close to those measured during the
CAPITOUL [] experiment.
In order to take into account the intraclass variability of
the ground temperature, a Gaussian white noise was added to
this parameter with a standard deviation of – K according
tothematerial.Incontrast,wedidnottakeintoaccountthe
intraclass variability of ground emissivity.
3.1.2. Atmospheric Proles Integration. We assume that the
scene dimensions are small enough to consider a spatially
uniform atmosphere over the image. e atmospheric species
(especially water vapor and ozone), the pressure, and the
temperature proles are set for the dierent altitudes of the
atmospheric layers. For this purpose we have used models
derived from radiosonde measurements.
Brown sandy loam
Asphalt
Bare red brick
Olive green paint
Aluminum
Green grass
Oxidized galvanized steel
Copper
Slate stone shingle
Concrete paving
F : Spatial distribution of the dierent ground materials com-
posing the scene.
At this stage, we generate a free-plume hyperspectral
image of the scene, based on MODTRAN calculations, using
COMANCHE soware [].
3.1.3. Gas Signature. e dierent gas species absorb light at
various wavelengths. is phenomenon depends on the elec-
tronic, vibrational,and rotational bands of the gas molecules.
In this study, we selected two pollutant gases with very
dierent radiative behavior. e sulfur dioxide (SO2)has
aspreadabsorptionspectrumonthe.–.mbandas
shown in Figure , while the ammonia (NH3)presents
several narrow spectral bands, especially for the wavelengths
10.42mand10.75m, which correspond to 960cm−1 and
930cm−1 in terms of wavenumber.
e absorption spectra of Figure  are taken from the high
resolution library of the PNNL. ese spectra were reduced
to a 5cm−1 spectral resolution to be consistent with typical
sensor spectral resolution.
3.1.4. Plume Distribution Simulation. In order to introduce
the plume’s radiative impact to the free-plume signal, we have
to model the D plume distribution in the scene, which is to
dene for each pixel of the plume the vertical prole of the
present gases.
ADMS-Aircra (Atmospheric Dispersion Modelling Sys-
tem) code [] was used to generate a Gaussian plume based
on the Brigg equation for plume dynamics []. e use
of ADMS-Aircra code requires the specication of some
inputs related to the scene geometry, the atmospheric and
meteorological conditions (in particular the wind speed and
direction), and the plume initial conditions like the release
rate/velocity/temperature.
Figure  shows the distribution of integrated concentra-
tion of a simulated SO2plume with the following parameters:
(i) outow rate (SO2): 222g/s,
(ii) outow rate (NH3): 11.39g/s,
(iii) stack height: 20m,
(iv) stack radius: 3m,
(v) plume ejection speed: 2m/s,

Journal of Spectroscopy 
285
290
295
300
305
310
315
320
(K)
(a)
Brown sandy loam
Asphalt
Bare red brick
Olive green paint
Aluminum
Concrete paving
Slate stone shingle
Copper
Oxidized galvanized steel
Green grass
0
0.2
0.4
0.6
0.8
1
Emissivity
850 900 950 1000 1050 1100 1150 1200 1250 1300800
Wavenumber (cm−1)
(b)
F : Ground parameters simulation. (a) Ground temperature map. (b) Emissivity spectra of materials present in the synthetic scene.
F : Synthetic renery scene without plume. Image in RGB
colors, representing the bands (R: 820cm−1,G:965cm−1,andB:
1165cm−1).
(vi) plume ejection direction: vertical,
(vii) wind speed: 2m/s.
A plume temperature distribution simulation is also needed
to introduce the plume’s radiative impact on the free-plume
signal. To introduce plume temperature distribution needed
to estimate the plume’s radiative impact on the free-plume
signal, we only set the gas exit temperature assuming that
, the dierence between the plume temperature (p)
and the initial ambient temperature (a), follows the same
distribution compared to the gas concentration []. In our
simulation we xed attheemissionsourceto300K.
e radiance signal of the plume-present scene is rep-
resented in Figure  and that of the plume-absent scene in
Figure . is signal is obtained using COMANCHE soware
that takes into account all the parameters described above.
0
0.5
1
1.5
SO2(∗2)
NH3
850 900 950 1000 1050 1100 1150 1200 1250 1300800
Wavenumber (cm−1)
×10−3
Absorbance (base-10)
F : Absorptive coecient spectra of sulfur dioxide (blue
curve) and ammonia (red curve).
3.2. Results and Discussion
3.2.1. Plume Detection. e rst step performed is the plume
detection.eSMFalgorithmwasappliedtwice:thersttime
for detecting SO2.eabsorbanceofthisgaswasusedto
model the associated target vector T.esecondtimethe
vector Twas taken equal to the absorbance of NH3.Aer
two thresholding operations on these results, we consider that
the plume region is the union of the two masks. Note that a
morphological opening operation was performed in order to
remove the detection artifacts.
Figure  represents the plume mask obtained at the end
of these treatments.
3.2.2. Classication of the Synthetic Scene. In this subsection,
we evaluate the eciency of the proposed classication
method. For this purpose, the confusion matrix and the
Cohen kappa coecient are used.

Journal of Spectroscopy
200 150 100 50 0
y(m)
050 100 150 200
x(m)
7186 ppm·m
0
2000
4000
6000
8000
Concentration (ppm·m)
F : Distribution of SO2concentration of the simulated plume,
with an outow rate of 222g/s and a wind speed of 2m/s.
F:SyntheticreneryscenewithaGaussianplumeofSO
2and
NH3. Image in RGB colors, representing the bands (R: 820cm−1,G:
965cm−1,andB:1165cm−1).
F : Plume detection mask for the synthetic renery scene.
In Figure , we illustrated the classication results on
the synthetic renery scene, both for the plume-absent area
(Figure (a)) and the plume-present area (Figure (b)).
Otherwise, in Table , we gured the confusion matrix
of the two classications realized. is matrix represents, for
each material present in the synthetic scene, its distribution
T : Confusion matrix of the classications performed on the
synthetic renery scene.
(a)
Material Classes of the plume-absent area

Green grass     
Brown sandy loam     
Olive green paint     
Asphalt     
Bare red brick     
Concrete paving     
Slate stone shingle     
Oxidized
galvanized steel     
Aluminum     
(b)
Material Classes of the plume-present area

Brown sandy loam    
Asphalt    
Bare red brick    
Concrete paving    
Copper    
Aluminum    
according to the obtained clusters. e classication of the
plume-absent region yields to  clusters, while the plume-
present classication leads to  clusters.
From Figure  and Table , one can notice that materials
could be sorted into three dierent families: Green grass,
{Aluminum +Copper},andtheothermaterialsofthescene.
is result is consistent with the ground parameters distri-
bution: the surface temperature of the Green grass is lower
than the temperature of other materials (see Figure (a)).
Moreover, aluminum and copper are reective materials,
unlike the other materials (see Figure (b)).
Inside the two last families of materials, the discrimina-
tion is quite dicult to achieve. Indeed, the radiances of those
materials are very close. Nevertheless, the performed classi-
cations are rather successful. e Cohen kappa coecient
is equal to 0.61for the plume-absent classication; the latter
equals 0.81for the plume-present classication. According to
the characterization done by Landis and Koch [] on the
values of the kappa coecient, our classications present a
substantial (0.61) agreement and an almost perfect agreement
(0.81).
3.2.3. Comparison of Background Radiance Estimation Meth-
ods. In order to compare the performance of the three meth-
ods used to estimate the background radiance, four pixels
throughtheplumewerepickedout.esepixels,belonging

Journal of Spectroscopy 
(a) (b)
F : Classication results on the synthetic renery scene. (a) Plume-absent region. (b) Plume-present region.
F : Positions of used pixels in the background radiance esti-
mation methods comparison.
to dierent classes derived from the classication (see Sec-
tion ..), are gured hereaer in Figure . e ground of
these pixels is composed, respectively, of brown sandy loam,
asphalt, aluminum, and copper.
Figure  summarizes the results of background radiance
estimation using the three methods: SB, CB, and CSB. For
eachoftheselectedpixelsarerepresentedtheon-plume
radiance (red), the real o-plume radiance (dotted green),
and the estimation of bkg using SB (cyan), CB (blue), and
CSB (magenta).
e cluster of brown sandy loam is the most present
among plume-absent pixels. us, the background properties
of the latter are strongly represented in the principal vectors
derived from the PCA. It is therefore obvious that the
SBmethodgivesanaccurateestimateofthebackground
radiance for pixels of this cluster (Figure (a)).
Furthermore, the background radiances of asphalt cluster
pixels are pretty close to the background radiances of brown
sandy loam cluster pixels. at is why bkg estimate given
by SB approach remains rather eective for this cluster
(Figure (b)).
Nonetheless, reective materials clusters have a back-
ground radiance much far from the main plume-absent clus-
ter, which aects signicantly the accuracy of the background
radiance estimation using SB, as we notice in Figures (c)
and (d).
We observe in these two last gures that, for such materi-
als, SB method reproduces approximately the high frequency
variations. However, there is a component similar to the main
cluster background radiance, which adds up to the estima-
tion.
ese curves indicate at one hand that the Selected-
Band approach yields an accurate estimate of the background
radiance, for the pixels of the most represented class among
plume-absent pixels. But on the other hand, for other classes,
the less the class is represented outside the plume, the less
its background radiance is correctly estimated. From these
observations, we deduce that SB method does not manage
well the case of heterogeneous background estimation.
Figure  shows that the introduction of a classication
to the background radiance estimation process improves the
results, especially for the minority classes of the scene. For
those pixels (Figures (c) and (d)), the two classication-
basedmethods(CBandCSB)giveamoreaccurateestimation
than SB does.
Onecannotethat,forpixel,thereisaslightdierence
between the real bkg radiance and the estimated one using
CB or CSB. is dierence comes from the fact that the class
#4is not represented at all in the plume-absent region. us,
it is assimilated during the classication with the class #3.
Regarding to the pixels 1and 2, the results of the method
CB are less specic than those of the SB method. Indeed, CB
method does not take into account the intraclass variability by
assimilating to each plume-present pixel the mean radiance
of plume-absent pixels belonging to the same class of the
latter. To this limitation, we must add the errors due to

Journal of Spectroscopy
2
4
6
8
10
12
14
900 1000 1100 1200 1300 1400800
Wavenumber (cm−1)
Radiance (𝜇W/sr/cm2/cm−1)
Lon
Lbkg
̃
Lbkg
̃
Lbkg
̃
LCSB
bkg
CB
SB
(a)
2
4
6
8
10
12
14
16
900 1000 1100 1200 1300 1400800
Wavenumber (cm−1)
Radiance (𝜇W/sr/cm2/cm−1)
Lon
Lbkg
̃
Lbkg
̃
Lbkg
̃
LCSB
bkg
CB
SB
(b)
0
2
4
6
8
10
12
900 1000 1100 1200 1300 1400800
Wavenumber (cm−1)
Radiance (𝜇W/sr/cm2/cm−1)
Lon
Lbkg
̃
Lbkg
̃
Lbkg
̃
LCSB
bkg
CB
SB
(c)
Lon
Lbkg
̃
LSB
bkg
̃
Lbkg
̃
LCSB
bkg
900 1000 1100 1200 1300 1400800
Wavenumber (cm−1)
0
2
4
6
8
10
12
14
Radiance (𝜇W/sr/cm2/cm−1)
CB
(d)
F : Comparison of background radiance estimation methods, for four dierent pixels through the plume. e red curves stand for the
on-plume radiances; the dotted green ones are the real background radiances. e cyan, blue, and magenta curves represent, respectively, the
background radiance estimated by the SB, CB, and CSB methods. (a) Results for pixel  (brown sandy loam), (b) results for pixel  (asphalt),
(c) results for pixel  (aluminum), and (d) results for pixel  (copper).
the missclassication. Despite these two sources of errors, the
CB background radiance estimation is still acceptable.
Concerning the CSB method, the estimation coincides
perfectly with the real background radiance, for those pixels.
is method manages well the intraclass variability.
In order to have a spatial visualization of the estimation
error of the three compared methods, we illustrated in Fig-
ure  the mean error of background radiance estimation. is
mean error was expressed in terms of brightness temperature.
Figure  upholds the undermentioned results. As
expected, with the SB approach, we obtain a mean error less
than 5K for the classes which are the most represented among
plume-absent pixels (#1and #2). is result conrms the
eciency of the approach on homogeneous scene. However,
for the two other classes, which are poorly (#3)ornot(#4)
represented among the plume-absent pixels, we reach more
than 45Koferror.
In the case of Clustering-Based methods, the mean error
obtained for the minority clusters is far smaller than the error
gotten with SB approach. rough class #4the mean error is
less than 4.5K, both for CB and CSB methods, despite the
fact that the latter is not represented among the plume-absent
pixels.
For the other classes, even class #3which presents more
than 35K of error with the SB approach, we hardly reach less
than 2.5K of error (CSB method). With the CB method, some
pixels have a mean error reaching 5.5K, but those pixels are
very few.

Journal of Spectroscopy 
0
10
20
30
40
(K)
(a)
1
2
3
4
5
(K)
(b)
0
1
2
3
4
(K)
(c)
F : Mean error of background radiance estimation, expressed in terms of brightness temperature. (a) Mean error obtained with the
Selected-Band estimation method. (b) Mean error obtained with the Clustering-Based estimation method. (c) Mean error obtained with the
Clustering-Based Selected-Band estimation method.
To assess the overall performance of these three methods,
the average error was calculated over the plume. As expected,
the CSB method is the best of the three methods: the mean
error obtained over the plume is equal to 0.48K. With the
CB method, the mean error remains low; it equals 0.80K.
However, the SB method gives a mean error of 9.55Kover
the plume. is is explained by the large error of estimation
for classes #3and #4.
Aer carrying out the three methods on synthetic data,
we can conclude that CSB approach provides better results
than CB and SB approaches, particularly regarding materials
not well, or not at all, represented among the plume-absent
pixels.
4. Application on Real Data
4.1.PresentationofTelopsHyper-CamAcquisition. e Telops
Hyper-Cam LW is a lightweight and compact imaging
instrument which uses Fourier Transfer Infrared (FTIR)
technology. e spectral resolution is user-selectable up to
0.25cm−1 over the 7.7to 11.7mspectralrange.eground-
based Telops Hyper-Cam is installed on a stabilization plat-
form equipped with a global positioning system (GPS) and
inertial motion unit (IMU). In a FTS imaging system, signal
modulation is achieved using a Michelson interferometer.
Acquiring a full interferogram typically lasts about one
second. erefore, an image motion compensation mirror
uses GPS/IMU data to compensate eciently for the aircra
movements during data acquisition.
is ight was carried out using a Hyper-Cam LW sensor
at an altitude of 685meters and a speed of 110knots leading
to a ground pixel size of 0.057m2/pixel. A spectral resolution
of 6cm−1 wasusedwhichgivesatotalof90spectral bands
equally spaced over the whole range cover by the focal pane
array detector. Outside temperature, wind speed, and relative
humidity at ground level were ∘C, 15km/h, and 37%,
respectively.

 Journal of Spectroscopy
1
2
3
(a)
NE
NE
NW
WS
SW
SE
(b)
F : Illustration of subimage and pixels used in the background radiance estimation methods comparison.
×10−3
0
0.2
0.4
0.6
0.8
1
900 950 1000 1050 1100 1150 1200 1250850
Wavenumber (cm−1)
Absorbance (base-10)
(a) (b)
F : Ethylene release detection. (a) Absorptive coecient spectrum of ethylene (from PNNL). (b) Plume detection mask for Telops
parking scene.
Airborne hyperspectral infrared measurements were car-
riedoutaboveapureethylenegasreleased.Ethyleneisa
ammable gas massively used worldwide in the production
of many polymer materials. During this experiment, gas was
released at a constant ow rate of approximately 20L/min.
4.2. Ground Radiance Estimation. Since the ethylene plume
coversagroundcomposedentirelyofasphalt,wereducedthe
size of the image to be processed, in order to limit the number
of classes obtained in the plume-absent area. is 100×100
subimageisrepresentedbytheredsquareinFigure.
4.2.1. Ethylene Presence Detection. e SMF algorithm was
applied on the Telops acquisition in order to dene the
ethylene release spatial extension. e ethylene’s absorbance
curve, illustrated in Figure (a), was used to model the target
vector T(see Section .).
A plume mask (Figure (b)) is obtained aer the applica-
tion of a threshold on the abundances image 𝛼. In addition,
we performed a morphological opening operation, in order
to take away the detection artifacts.
Unfortunately the applied morphological opening
removes some plume-present pixels, which are localized at
the frontier of the plume.
4.2.2. Classication of Telops parking Scene. As opposed to the
synthetic scene case, we cannot have a quantitative evaluation
of the classication. us, only a qualitative description of it
is given thereaer.
On this acquisition performed around  a.m., one can
notice the presence of a temperature gradient along the

Journal of Spectroscopy 
0
10
20
30
40
50
(a)
0
1
2
3
(b)
F : Classication results on Telops parking scene. (a) Plume-absent region. (b) Plume-present region.
southeast to northwest direction. Indeed, the sun, while rising
inthesky,heatedgraduallythescene.us,eveniftwopixels
are composed from the same material, they could have two
dierent ground temperature, according to their location in
the scene. Consequently, those pixels should be classied into
two dierent clusters.
Figure  shows the classication results obtained on
Telops’ parking scene. e classication on the plume-absent
region is illustrated in Figure (a), while the classication
involving the plume-present region is illustrated in Fig-
ure (b).
e plume-present region was clustered into 3classes,
while the plume-absent region was clustered into 57classes.
From these two gures, we notice that the classica-
tion complies with the temperature gradient. Note however
that the classication in the plume-present region is more
accurate than the second classication. Indeed, the plume-
absent classes corresponding to the plume-present classes #2
(yellow) and #3(brown) were merged into the same class. is
can be explained by the fact that we used a threshold on the
size of class (max) higher in the plume-absent case, in order
to reduce the number of classes.
4.2.3. Comparison of Background Radiance Estimation Meth-
ods. For this scene, we do not have any aprioriknowledge
of the background radiance. But, by observing the scene, we
cannoticethatitseemstobehomogeneousalongthevertical
direction.Inotherwords,itisjustiedtoassumethatbkg
is vertically constant. Hence, for a given plume-present pixel,
we approximate its background radiance by the mean spectra
of some plume-absent pixels located at the same column than
thelatter.isradiancewillbedesignatedbythetermo .
Figure  shows the results of background radiance
estimation using the three methods: SB, CB, and CSB. For
the three selected pixels, we gured the on-plume measured
radiances (red curve), the expected o-plume radiances
(dotted green curve), and the estimation of bkg using SB
(cyan), CB (blue), and CSB (magenta).
e rst point we can deduce from Figure  is the
relevance of the radiance o to model the background
radiance. One can notice that it agrees quite well with the on-
plumeradianceonbandswheretheabsorbanceofethyleneis
close to zero. Moreover, the dierence between o and on
on bands of ethylene absorption follows the same variation
then the absorption curve of ethylene.
For the three chosen pixels, the background radiance
estimation obtained by both CB and CSB methods is rather
consistent with o . Nonetheless, the SB estimate does not
matchwellwiththeexpectedradiance.Forpixels#1and #2
SB approach underestimates the background radiance, while
it overestimates bkg for pixel #3.
ose estimation errors are distributed over the whole
spectral range. ey are more important for ethylene absorp-
tion features.
So as to get an idea of the error magnitude for each
method, two parameters measuring this error with respect to
the expected radiance were dened: the root mean square of
the brightness temperature error (𝑇b) is calculated, for each
pixel, as follows:
𝑇b(K)=1
B⋅
bkg −o ⋅
bkg −o 𝑇,()
where 
bkg is the background brightness temperature esti-
mated by one of the three methods, for the concerned pixel.
o is the expected background brightness temperature, for
pixel in question.
Moreover,wedenetherelativerootmeansquareerror
on radiance (𝐿)by
𝐿(%)
=1
B⋅
bkg −o 
o ⋅
bkg −o 
o 𝑇,()

 Journal of Spectroscopy
⟨Loff⟩
4
6
8
10
12
14
16
900 950 1000 1050 1100 1150 1200 1250 1300850
Wavenumber (cm−1)
Radiance (𝜇W/sr/cm2/cm−1)
Lon
̃
LCSB
bkg ̃
Lbkg
CB
̃
Lbkg
SB
(a)
4
6
8
10
12
14
16
850 950 1000 1050 1100 1150 1200 1250 1300900
Wavenumber (cm−1)
Radiance (𝜇W/sr/cm2/cm−1)
⟨Loff⟩ L on
̃
LCSB
bkg ̃
Lbkg
CB
̃
Lbkg
SB
(b)
4
6
8
10
12
14
16
18
900 950 1000 1050 1100 1150 1200 1250 1300
850
Wavenumber (cm−1)
Radiance (𝜇W/sr/cm2/cm−1)
⟨Loff⟩ L on
̃
LCSB
bkg ̃
Lbkg
CB
̃
Lbkg
SB
(c)
F : Comparison of background radiance estimation methods, for three dierent pixels through the plume. e red curves stand for the
on-plume radiances; the dotted green ones are the expected background radiances. e cyan, blue, and magenta curves represent, respectively,
the background radiance estimated by the SB, CB, and CSB methods. (a) Results for pixel , (b) results for pixel , and (c) results for pixel .
where 
bkg is the background radiance estimated by one of
the three methods, for the concerned pixel.
Weguredtheobtainedresults,foreachofthethree
pixels, in Table .
Table  validates the conclusions deduced from Figure .
e SB method gives a less accurate estimation than the
Clustering-Based methods. If for pixel #1,themeanerror
calculated is three times higher with the SB method, it
becomes ten times higher for pixels #2and #3.Otherwise,
the CB method has a background radiance estimation almost
as similar as the CSB method estimation. Beside for pixel #1,
the estimation obtained by the CB method is better than that
obtained by CSB method. Moreover, the average error of all
plume-present pixels is equal to 0.64KfortheCBmethod,
while it is equal to 0.68K for the CSB method. However the
two methods remain of the same order of magnitude.
Recall, nevertheless, that o is just an approximation
of the real o . us, the result presented below does
not induce necessarily that CB method is better than CSB
method.
Figure  illustrates a comparison of dierent radiances
attheethylenemostabsorptiveband(950.4cm−1), for pixels
along a horizontal cross section. Pixels from  to  are
plume-present pixels. erefore, the radiances comparison is
restricted to those pixels.
Figure  shows that the SB approach miscalculates the
background radiance, comparing to the other methods. On
a part of plume-present pixels, it overestimates bkg ,whileit
underestimates this term on the other parts of plume-present
pixels. e estimation error reaches at most 10%forthisband.
Recall that this band is the most important for the ethylene
quantication (see Figure (a)).

Journal of Spectroscopy 
T : Evaluation of the dierence between expected background
radiance and estimated background radiance, using one of the three
methods used in this paper. e rst table presents the root mean
square of the brightness temperature error (𝑇b), while the second
summarizes the results in terms of the relative root mean square
error on radiance (𝐿).
(a)
𝑇b(K) Selected pixels

SB 1.96 3.32 3.94
CB 0.36 0.44 0.46
CSB 0.5 0.29 0.4
(b)
𝐿(%) Selected pixels

SB 3.1 5.06 6.21
CB 0.55 0.69 0.68
CSB 0.95 0.5 0.67
Radiance (𝜇W/sr/cm2/cm−1)
12
12.5
13
13.5
14
14.5
15
15.5
16
10 20 30 40 50 60 70 80 90 1000
X
Plume detected
⟨Loff⟩ L on
̃
LCSB
bkg ̃
Lbkg
CB
̃
Lbkg
SB
F : Comparison of dierent radiances at the ethylene
absorptive band (950.4cm−1), along a horizontal cross section
containing some plume-present pixels. e red curve stands for the
on-plume radiances; the green dotted one is the expected back-
ground radiances. e cyan, blue, and magenta curves represent,
respectively, the background radiances estimated by the SB, CB, and
CSB methods.
As expected, the radiance estimated using CB method is a
constant piecewise function. We can see that, for the rst class
(from the le), the estimated radiance is consistent with the
mean of the expected radiance (o )of concerned pixels.
Butforthesecondclass,whichistheresultofmergingoftwo
classes (see Figure ), the estimated radiance does not match
perfectlywiththemeanofo .Usingabetterclassication
of the plume-absent region, it is possible to sort this second
class into two classes, which improves the estimation yielded
by CB method.
In Figure , we observe that CSB method takes into
consideration the intraclass variability, which allows getting
better estimation with this method than CB method. For
the concerned band, CSB method does not exceed 3%of
estimation error.
In order to generalize those observations to the all plume-
present pixels, we illustrated in Figure  a comparison of
the background radiance estimation obtained by each of the
three methods. is comparison is performed at the band
950.4cm−1.
One can notice that at the frontier of the plume, some
plume-present pixels have a relatively low radiance (dark
pixels).isisduetoabadplumedetectioninthisregionas
we already explained it above. For those pixels, the radiance
represented in Figure  is on and not bkg.
Figure (a) shows that SB method overestimates the
background radiance on a part of plume-present pixels
(bright area of the plume). On another part of plume-present
pixels, bkg is underestimated (dark area of the plume). is
is due to the presence in the plume-absent region of more
or less shinny materials than the plume-present pixels. e
signal of those materials is then integrated in the principal
components derived from the PCA.
e Clustering-Based methods use only the signal of
plume-absent pixels having the same background properties
than the plume-present pixels. e use of only pertinent
information for the background radiance estimation there-
fore allows improving its accuracy.
is is clearly visible in Figure , since we note a certain
homogeneity between the value of the plume-present and the
plume-absent radiance.
4.3. Gas Concentration Estimation. From the scene described
in Figure , we rst compute an atmospheric compensation;
then we apply a linear algorithm to estimate ethylene concen-
tration for each background estimation.
Atmospheric compensation stage has two goals: rst it
aims to avoid the introduction of a probable bias from
atmospheric nontarget gases on the retrieval; then it allows
the estimation of the atmospheric ground level tempera-
ture and water vapor concentration. We assume here that
atmosphere properties are homogeneous over the scene. We
applied a Spectral Smoothness (SpSm) algorithm [, ] on
a homogeneous subimage to estimate atmospheric proles
(temperature, water vapor), surface emissivity, and surface
temperature.
e SpSm algorithm from a set of initial guess is used to
reduce retrieved emissivity spectral variability on homoge-
neous area of concrete material. e initial set is composed
with an atmospheric prole of temperature and water vapor
from “Quebec meteorological center” tted with local mea-
surement (294.15K for atmospheric ground temperature and
37% for relative humidity) and ground temperature obtained
from the highest value of spectral brightness temperature
measured on the scene. We use  tiny variations of atmo-
spheric proles and  dierent ground level temperatures to
nd the optimal set of parameters which leads to low spectral
variation of retrieved spectral emissivity. For this concrete
subimage the corresponding retrieved spectral emissivity is

 Journal of Spectroscopy
(a) (b)
(c)
F : Comparison of the three background radiance estimations according to the band 950.4cm−1, where the ethylene absorbance is
the most important. (a) Selected-Band approach. (b) Clustering-Based method. (c) Clustering-Based Selected-Band method.
shown in Figure . e corresponding ground temperature,
ground level atmospheric temperature, and water vapor con-
centration are, respectively, 316.5K, 296.6K, and 10200ppm.
From this atmospheric prole we compute atmospheric
transmission and atmospheric radiance used for the atmo-
spheric correction pixel by pixel.
Finally, the simple quantication algorithm used is from
a linear model of the dierential signature:
L=Lon −Lo =⋅A(𝜆)⋅BTplume ,𝜆−Lo , ()
where Tplume is the plume temperature, is the column
integrated concentration (ppm⋅m), and B(T,𝜆)is the Planck
function. One can estimate the concentration applying for
eachpixelbythefollowingequation:
=A(𝜆)⋅BTplume ,𝜆−Lo ,
=T𝑇Σ−1
XL
T𝑇Σ−1
XT.()
900 950 1000 1050 1100 1150850
Wavenumber (cm−1)
0.86
0.88
0.9
0.92
0.94
0.96
0.98
1
Ground emissivity
F : Mean ground spectral emissivity retrieved through the
subimage.
Plume temperature is assumed to be homogeneous and
equal to ground level atmospheric temperature estimated

Journal of Spectroscopy 
0
100
200
300
400
(ppm·m)
(a)
0
50
100
150
200
250
300
350
400
(ppm·m)
(b)
0
100
200
300
400
500
(ppm·m)
(c)
F : Retrieved ethylene concentration (ppm⋅m) from the three estimated Lo images. (a) Selected-Band approach. (b) Clustering-Based
method. (c) Clustering-Based Selected-Band method.
to be 296.65K. One can notice than neither pixel-by-pixel
emissivity nor ground temperature is needed here to estimate
gas concentration.
e dierent stages described above are applied to the
estimated Lo images shown in Figure .
Figuresandshowsethyleneconcentrationretrieved
from Hyper-Cam data using the three estimated background
methods outlined above and their dierences. e mean
retrieved integrated concentration is about 200ppm by CSB
method. One can notice that ground radiance main dier-
ences are translated into retrieved concentration dierences.
In particular, the upper le corner of the plume where the
background radiance was overestimated by about 10%by
SB method leads to the highest dierences in concentration
(up to  ppm⋅m). en, class borders used for CB method
where radiance dierence was the highest with CSB method
lead to local dierences of about  ppm⋅m. e mean
dierence between CB and CSB methods is less than 10%
in concentration whereas it climbs up to 20% between SB
and CSB methods. As pixel ground level size is about 23cm
the plume mean width size orthogonal to wind direction is
calculated to 4m and average mass in one-meter long slice of
the plume is calculated to be 0.986g assuming ethylene molar
weight wm of 28g/mol. e ow rate can be estimated
to be 4.2g/s assuming a wind speed value of 4.3m/sand
using the following equation where (in ppm⋅m) is the mean
integratedcolumnconcentrationinanorthogonalsliceofone
meter thick and 4m width. is results ts well with the true
value of 20L/min which corresponds to 3.15g/s assuming
that ethylene volume weight is 567.65200kg/m3:
=⋅⋅103⋅
22.71.()
5. Summary and Conclusions
Gas trace plume remote sensing above industrial scene
requires both high spectral and spatial resolution. Using
airborne FTS imaging techniques it becomes possible to
detect and quantify gas traces. However retrieval accuracy
depends on both pixel-by-pixel background under plume

 Journal of Spectroscopy
0
50
100
150
200
(ppm·m)
(a)
0
10
20
30
40
50
60
70
80
(ppm·m)
(b)
F : Comparison between retrieved concentration from the dierent approaches. (a) Dierence between retrieved concentration from
SB background estimation and CSB background estimation. (b) Dierence between retrieved concentration from CB background estimation
and CSB background estimation.
estimation and good enough spectral resolution around
target gas absorption peak. In this paper we propose a
method to estimate ground radiance pixel by pixel taking
into account scene variability spectral behavior. e CSB
method described above is a Clustering-Based method which
aims to associate statistical spectral properties from classes
nonimpacted by the plume to classes below the target gas
plume.ismethodisbasedonSBmethodalgorithm[]
extended to a clustering approach. We have shown that
introducing an initial classication of the scene improves
background radiance estimation for nonhomogeneous scene
in comparison with classical SB method or simple Clustering-
Based method. Results based on simulations show more than
10K in brightness temperature for low emissivity material
and up to 3K for high emissivity material.
e CSB method applied to airborne Hyper-Cam LW
dataacquiredaboveanethylenereleaseof20L/min shows
that the CSB method can reduce background radiance uncer-
tainty from 5to 1%orfrom3to  K in terms of brightness
temperature uncertainty, for a high emissivity materiel such
as concrete. is improvement leads to a mean dierence of
about 10%onethyleneplumeretrievedconcentrationsinthis
particular “easy” scene.
Finally we propose in this paper an end-to-end method
using a single hyperspectral image to estimate (i) ground
radiance and properties (emissivity and temperature); (ii)
atmospheric ground level temperature and water vapor
content; and (iii) trace gas plume concentration with an
encouraging accuracy. Indeed the retrieved ow rate is close
to mean ow rate during the gas release.
e method outlined above must now be tested on
industrial scenes where expected improvement should be
higher as it deals well with a very high number of materials,
with intraclass variability such as shadow and temperature
gradient and with low emissivity materials.
Symbols
Plume Detection
:Numberofpixels
B:Numberofspectralbands
X:Hyperspectralimagematrix
[×B].Xcould represent radiance
(L) or brightness temperature (b)
x:ApixelofX
x:MeanspectrumofX
ΣX:CovarianceofX
T: e gaseous target spectrum
𝛼:Targettcoecients(abundances)
d:Residualvector.
Selected-Band Approach
on: Number of plume-present pixels
o:Numberofplume-absentpixels
SB:Numberofselectedbands
p:Numberoftheusedprincipalcomponents
on(): On-plume radiance: measured radiance
for a plume-present pixel
o (): O-plume radiance: measured radiance
for a plume-absent pixel
bkg(): Background (plume-free) radiance for a
pixel.
Classication
max:resholdonthesizeofaclass
C:Numberofclasseswithoutplume
CP: Number of classes containing plume.

Journal of Spectroscopy 
Competing Interests
e authors declare that they have no competing interests.
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