Estimating gas quantity in a pixel based on spectral matched filtering
Gas quantity in a pixel may be estimated based on spectral matched filtering. Image data associated with a scene may be received. The scene may comprise a plurality of pixels. Next, a spectral matched filter may be constructed for a predetermined gas and based on the image data. A quantity of the predetermined gas may then be estimated in at least one of the plurality of pixels by applying the spectral matched filter to the image data.
1 . A method comprising:
receiving image data associated with a scene, wherein the scene comprises a plurality of pixels;
constructing a spectral matched filter for a predetermined gas based on a scene average spectrum L and a scene spectral covariance C from the image data; and
estimating a quantity of the predetermined gas in at least one of the plurality of pixels by applying the spectral matched filter to the image data,
wherein the spectral matched filter f comprises:
f
=
α
(
L
¯
-
L
↑
)
C
-
1
α
(
L
¯
-
L
↑
)
C
-
1
[
α
(
L
¯
-
L
↑
)
]
T
;
and
wherein α is a spectral absorption of the gas and L ↑ is atmospheric scattered light in the scene.
2 . The method of claim 1 , wherein the scene average spectrum in a spectral band i comprises:
L
¯
i
=
∑
k
=
all
pixels
L
i
,
k
number
of
pixels
.
3 . The method of claim 1 , wherein the scene spectral covariance comprises:
C
i
,
j
=
1
number
of
pixels
∑
k
=
all
pixels
(
L
i
,
k
-
L
¯
i
)
(
L
j
,
k
-
L
¯
j
)
.
4 . The method of claim 1 , wherein constructing the spectral matched filter comprises constructing the spectral matched filter based on in-scene statistics optimally aligned with spectral features of the predetermined gas relative to the scene spectral covariance.
5 . The method of claim 1 , wherein the quantity of the predetermined gas comprises:
n
c
=
-
1
2
f
(
L
-
L
↑
)
T
.
6 . The method of claim 1 , wherein the image data comprise spectral quantities representing spectral features in a Shortwave Infrared (SWIR) spectral range.
7 . The method of claim 1 , wherein the image data comprise spectral quantities representing spectral features in at least one of the following ranges: 1195 nm-1225 nm, 1550 nm-1590 nm, 1640 nm-1680 nm, 1710 nm-1750 nm, 2145 nm-2185 nm, 2185 nm-2225 nm, 2235 nm-2285 nm, and 2295 nm-2365 nm.
8 . The method of claim 1 , wherein the predetermined gas is methane.
9 . A system comprising:
a memory storage; and
a processing unit coupled to the memory storage, wherein the processing unit is operative to:
receive image data associated with a scene, wherein the scene comprises a plurality of pixels;
construct a spectral matched filter for a predetermined gas based on a scene average spectrum L and a scene spectral covariance C from the image data; and
estimate a quantity of the predetermined gas in at least one of the plurality of pixels by applying the spectral matched filter to the image data,
wherein the spectral matched filter f comprises:
f
=
α
(
L
¯
-
L
↑
)
C
-
1
α
(
L
¯
-
L
↑
)
C
-
1
[
α
(
L
¯
-
L
↑
)
]
T
;
and
wherein α is a spectral absorption of the gas and L ↑ is atmospheric scattered light in the scene.
10 . The system of claim 9 , wherein the scene average spectrum in a spectral band i comprises:
L
¯
i
=
∑
k
=
all
pixels
L
i
,
k
number
of
pixels
.
11 . The system of claim 9 , wherein the scene spectral covariance comprises:
C
i
,
j
=
1
number
of
pixels
∑
k
=
all
pixels
(
L
i
,
k
-
L
¯
i
)
(
L
j
,
k
-
L
¯
j
)
.
12 . The system of claim 9 , wherein the processing unit is operative to construct the spectral matched filter based on in-scene statistics optimally aligned with spectral features of the predetermined gas relative to the scene spectral covariance.
13 . The system of claim 9 , wherein the quantity of the predetermined gas comprises:
n
c
=
-
1
2
f
(
L
-
L
↑
)
T
.
14 . The system of claim 9 , wherein the image data comprise spectral quantities representing spectral features in a Shortwave Infrared (SWIR) spectral range.
15 . A non-transitory computer-readable medium that stores a set of instructions which, when executed, perform a method comprising:
receiving image data associated with a scene, wherein the scene comprises a plurality of pixels;
constructing a spectral matched filter for a predetermined gas based on a scene average spectrum L and a scene spectral covariance C from the image data; and
estimating a quantity of the predetermined gas in at least one of the plurality of pixels by applying the spectral matched filter to the image data,
wherein the spectral matched filter f comprises:
f
=
α
(
L
¯
-
L
↑
)
C
-
1
α
(
L
¯
-
L
↑
)
C
-
1
[
α
(
L
¯
-
L
↑
)
]
T
;
and
wherein α is a spectral absorption of the gas and L ↑ is atmospheric scattered light in the scene.
16 . The non-transitory computer-readable medium of claim 15 , wherein the scene average spectrum in a spectral band i comprises:
L
¯
i
=
∑
k
=
all
pixels
L
i
,
k
number
of
pixels
.
17 . The non-transitory computer-readable medium of claim 15 , wherein the scene spectral covariance comprises:
C
i
,
j
=
1
number
of
pixels
∑
k
=
all
pixels
(
L
i
,
k
-
L
¯
i
)
(
L
j
,
k
-
L
¯
j
)
.
18 . The non-transitory computer-readable medium of claim 15 , wherein constructing the spectral matched filter comprises constructing the spectral matched filter based on in-scene statistics optimally aligned with spectral features of the predetermined gas relative to the scene spectral covariance.
19 . The non-transitory computer-readable medium of claim 15 , wherein the quantity of the predetermined gas comprises:
n
c
=
-
1
2
f
(
L
-
L
↑
)
T
.
20 . The non-transitory computer-readable medium of claim 15 , wherein the image data comprise spectral quantities representing spectral features in at least one of the following ranges: 1195 nm-1225 nm, 1550 nm-1590 nm, 1640 nm-1680 nm, 1710 nm-1750 nm, 2145 nm-2185 nm, 2185 nm-2225 nm, 2235 nm-2285 nm, and 2295 nm-2365 nm.