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50 3. Standard destriping techniques and application to MODIS
Table 3.3 – Mean Kolmokorov-Smirnov detectors distance for bands 27, 30
and 33 for Terra MODIS and 27, 30 and 36 for Aqua MODIS
– Terra Aqua
Detector Band 27 Band 30 Band 33 Band 27 Band 30 Band 36
d 1 0.3544 0.1108 0.0413 0.0265 0.0114 0.0189
d 2 0.1637 0.0253 0.0150 0.0253 0.0113 0.0142
d 3 0.1624 0.0261 0.0149 0.0338 0.0120 0.0192
d 4 0.1604 0.0253 0.0140 0.0246 0.0130 0.0139
d 5 0.1562 0.0312 0.0181 0.0245 0.0111 0.0114
d 6 0.1579 0.0273 0.0130 0.0278 0.0111 0.0106
d 7 0.1973 0.0259 0.0154 0.0255 0.0106 0.0118
d 8 0.2188 0.0429 0.0142 0.0958 0.0125 0.0135
d 9 0.3195 0.0260 0.0218 0.0353 0.0134 0.0134
d 1 0 0.2587 0.0248 0.0152 0.0514 0.0379 0.0140
where P i and P j are the ECDFs of detectors i and j, and r(n) is the set of radiances
observed by both detectors. The Kolmogorov-Smirnov distance measures the distributional
distance for every couple of detectors and can be averaged for a single detector i ≠ j as :
D i =
1
card(M i ) − 1
∑
D i,j
(3.13)
where M i is the set of detectors. [Antonelli et al., 2004] and [di Bisceglie et al., 2009],
specify that the classification of detectors and the selection of a reference one is determined
from both BTBDD and Kolmogorov-Smirnov distances. However, it is not mentioned how
this is done. As an alternative, we will rely only on the Kolmogorov-Smirnov distances ;
the weakest value D M i
i
determines the reference detector to be used for the radiometric
equalization. Let us denote by B r (n) and B i (n) the set of radiances measured in the
bowtie region by a reference detector r and a noisy detector i. The equalization function
is obtained with a polynomial regression between B r (n) and B i (n) :
j∈M i
j≠i
B r (n) =p 0 + p 1 .B i (n)+p 2 .B 2 i (n)+... + p N .B N i (n) (3.14)
where p 0 , p 1 ...p N are the coefficients of the best fitting polynome. The radiometric equalisation
of the signal I i (n) measured by the detector i over the entire swath is then corrected
as :
Î i (n) =p 0 + p 1 .I i (n)+p 2 .I 2 i (n)+... + p N .I N i (n) (3.15)
All the other detectors are corrected with the same procedure. Destriping results obtained
with the OFOV technique are illustrated in figure 3.7. When the equalization is based on
polynomial functions of order 1, the OFOV method might be comparable to the moment
matching technique because only the affine response of the detectors is modified. However,
while moment matching is based on statistical assumptions satisfied only over homogeneous
areas, the OFOV method relies entirely on the bowtie effect to equalize the detectors