Method to analyze remotely sensed spectral data
View Patent ↗A fast and rigorous multivariate curve resolution (MCR) algorithm is applied to remotely sensed spectral data. The algorithm is applicable in the solar-reflective spectral region, comprising the visible to the shortwave infrared (ranging from approximately 0.4 to 2.5 μm), midwave infrared, and thermal emission spectral region, comprising the thermal infrared (ranging from approximately 8 to 15 μm). For example, employing minimal a priori knowledge, notably non-negativity constraints on the extracted endmember profiles and a constant abundance constraint for the atmospheric upwelling component, MCR can be used to successfully compensate thermal infrared hyperspectral images for atmospheric upwelling and, thereby, transmittance effects. Further, MCR can accurately estimate the relative spectral absorption coefficients and thermal contrast distribution of a gas plume component near the minimum detectable quantity.
1. A method to analyze remotely sensed spectral data, comprising:
(a) acquiring a remotely sensed spectral data set, X;
(b) modeling the data set according to X=C true S true T+1a T +E instr , where C true is a matrix of true abundances for components contained within a remote scene, S true is a corresponding matrix of true spectral endmembers for the components, T is a matrix of atmospheric transmittance values, 1 is a vector of ones, a T is a vector representing an additive, atmospheric component, and E instr is a matrix describing instrument noise;
(c) calculating the atmospheric transmittance matrix T and additive atmospheric component a T to provide an atmospherically compensated data set according to X c =(X−1a T )T −1 =C true S true +E instr ; and
(d) obtaining a multivariate curve resolution (MCR) estimate of C true and S true , subject to constraints.
2. The method of claim 1 , wherein the data set X comprises solar-reflective spectral data.
3. The method of claim 1 , wherein the data set X comprises midwave infrared spectral data.
4. The method of claim 1 , wherein step (d) comprises Principal Component Analysis (PCA) factorization of the atmospherically compensated data set X c , rotation of the PCA factors to provide a rotated abundance matrix {tilde over (C)} and a rotated endmember matrix {tilde over (S)}, and MCR of the rotated abundance and endmember matrices to obtain the estimates of C true and S true .
5. The method of claim 4 , wherein the PCA factorization comprises nonlinear iterative partial least squares, eigenanalysis, or singular value decomposition.
6. The method of claim 4 , wherein the rotation of the PCA factors comprises Quartimax or Varimax rotation.
7. A method to analyze remotely sensed spectral data, comprising:
(a) acquiring a remotely sensed thermal infrared data set, X;
(b) modeling the data set according to
X
=
GKT
+
BFT
+
1
I
u
T
+
E
instr
=
[
G
B
1
]
[
KT
FT
I
u
T
]
+
E
instr
,
where G is a matrix of thermal contrast coefficients for plume gases, K is a matrix of spectral absorption coefficients for the plume gases, B is a matrix of amplitude coefficients for solids, F is a matrix of spectral coefficients for the solids, T is a diagonal matrix of atmospheric transmittance values, 1 is a vector of ones, and I u T is a vector containing atmospheric upwelling terms, and E instr is a matrix describing instrumental noise;
(c) obtaining a multivariate curve resolution (MCR) estimate of the atmospheric upwelling I u T , subject to constraints;
(d) calculating the atmospheric transmittance matrix T to provide an atmospherically compensated data set according to
X
c
=
(
X
-
1
I
u
T
)
T
-
1
=
GK
+
BF
+
E
instr
=
[
G
B
]
[
K
F
]
+
E
instr
=
C
true
S
true
+
E
instr
;
and
(e) obtaining an MCR estimate of G, K, B, and F, subject to constraints.
8. The method of claim 7 , wherein the constraint in step (c) comprises a constant abundance constraint.
9. The method of claim 7 , wherein step (d) comprises estimating the atmospheric transmittance matrix T according to ε s (λ)τ(λ)=( x (λ)−I u (λ))/B s (λ, T ), where ε s (λ) is the mean surface emissivity over all the pixels at wavelength λ, T is the mean surface temperature over all the pixels, B s (λ, T ) is the Planck blackbody radiance function evaluated at wavelength λ and the mean surface temperature T , τ(λ) is the atmospheric transmittance at wavelength λ, and I u (λ) is the atmospheric upwelling at wavelength λ.
10. The method of claim 7 , wherein step (e) comprises Principal Component Analysis (PCA) factorization of the atmospherically compensated data set X c , rotation of the PCA factors to provide a rotated abundance matrix {tilde over (C)} and a rotated endmember matrix {tilde over (S)}, and MCR of the rotated abundance and endmember matrices to obtain the estimates of G, K, B, and F.
11. The method of claim 10 , wherein the PCA factorization comprises nonlinear iterative partial least squares, eigenanalysis, or singular value decomposition.
12. The method of claim 10 , wherein the rotation of the PCA factors comprises Quartimax or Varimax rotation.