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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
51 Figure 3.8 – (Left) Noisy image from Terra MODIS band 27 (Right) Image destriped with the IFOV method response. To this extent, the OFOV method can be viewed as a radiometric calibration procedure. It is worth mentionning that only the range of radiances contained in the bowtie region is corrected and additional processing is required to cover the entire dynamic range of the acquired signal. In our implementation, the equalization functions were derived from measurements with scan angles higher than ±25˚. Linear and quadratic fitting computed on the selected images showed little differences and only first order polynomes were used. Radiance values not contained in the bowtie region were not equalized. 3.5 Frequency filtering Frequency filtering methods has been widely used for the elimination of stripes on satellite images. [Srinivasan et al., 1988] proposed a new approach for Landsat TM and MSS based on a spectral analysis of the stripe noise. Despite extensive research in this direction [Crippen, 1989], [Simpson et al., 1995], [Simpson et al., 1998], [Chen et al., 2003] and good visual results on GOES and Landsat sensors, frequency filtering can only be viewed as a cosmetic improvement. The smoothed results obtained with low-pass filtering can nonetheless be used as a reference to compare the performances of other detriping techniques. In this subsection, we briefly explore the application of frequency filtering on MODIS data. 3.5.1 Spectral Analysis In most cases, striping can be considered as a periodic noise. The application of a lowpass filter (an averaging filter in the spatial domain for exemple) reduces the visual impact
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134 BIBLIOGRAPHIE P. Perona and J.
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