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120 5. Application : Restoration of Aqua MODIS Band 6 1 1 0.8 0.8 Simulated NDSI 0.6 0.4 0.2 0 −0.2 Simulated NDSI 0.6 0.4 0.2 0 −0.2 −0.4 −0.4 −0.6 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 Measured NDSI −0.6 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 Measured NDSI Simulated NDSI 1 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 Measured NDSI Figure 5.8 – Scatter plots of simulated and measured NDSI from Terra MODIS band 6 (Labrador) (Left) Local interpolation (Right) Global interpolation (Bottom) Spectral inpainting posed approache refered to hereafter as spectral inpainting. The locations of these scenes coincide with those used in the work of [Salomonson and Appel] where MODIS data were used to estimate fractional snow cover. We recall that detectors of Terra MODIS band 6 are all functional and therefore, restoring algorithms described above are applied on images where measurements from 4 detectors have been set to zero to simulate non functional detectors. The true and estimated images for Terra band 6 are then combined with band 4 data in order to compute the NDSI index. The resulting measured and simulated NDSI indexes are then compared in terms of absolute mean difference, root mean square error and correlation coefficients to evaluate the efficiency of each approach. Results are reported in table . Let us mention few notes on the computational aspect of the spectral inpainting method. In practice, for a missing pixel x from band 6, a window of limited size (instead of the entire image domain Ω) is used to determine the spectral similarity between its pixels and pixel x. Since the proposed approach does not relie on spatial information, standard periodic or symmetric extensions of boundaries cannot be used. Instead, the search window can
e square or rectangular depending on the position of the pixel with respect to the image borders. Alternatively, the image can be fragmented into blocks of K × K pixels and the algorithm is applied separately for each block with a search window composed of the entire domain of the subimage. The choice of K then depends on the available computational power. Results illustrated in this study were obtained with K = 200. Another pratical aspect of the spectral inpainting method lies in the selection of the parameter N in equation (5.20). The choice N = 1 holds a physical meaning and ensures radiometric coherence as it corresponds to the case where a missing pixel from band 6 is given the same value as the most spectrally similar available pixel in the same band. Furthermore, all spectral bands (3, 4, 5, 6 and 7) have been destriped prior to the restoration procedure and, therefore all measurements used in the spectral inpainting can be assumed to be noise free. The spectral similarity measures defined in the previous section have all been tested except the Spectral Correlation Measures which requires overlapping spectral bands. The two existing techniques for the restoration of Aqua MODIS band 6 are entirely based on the correlation of measurements between bands 6 and 7. The global polynomial regression proposed in [L. L. Wang and Nianzeng] only applies to snow covered regions and do not make any distinction in land cover types. Estimation of band 6 missing lines via equations (5.3) results in strong striping in the restored image even over snow covered areas. Improved results are obtained when the global polynomial relationship between band 6 and 7 is estimated using data from the current swath. Another limitation of the global interpolation method proposed by Wang et al., is attached to the assumption that the relationship between bands 6 and 7 of Terra MODIS can be directly transposed to Aqua MODIS. In pratice, this assumption do not hold because of calibration differences between Terra and Aqua MODIS instruments. The local interpolation procedure described in [Rakwatin et al.] is a refinement of the global interpolation. To account for land cover types, the estimation of missing pixels is derived from a polynomial regression between bands 6 and 7, restricted to a local windows. Results achieved with this technique are often disapointing, as confirmed by the strong striping visible in the restored band 6. This can be attributed to the incoherent mixing of spatial and spectral information. Indeed, the value of a dead pixel from band 6 is determined from minimum and maximum values of band 7 in a local window, which actually correspond to spectrally distant pixels. With such a procedure, the spatial locality does not garantee any distinction in land cover types. On the contrary, the approach of [Rakwatin et al.] amounts to a spatio-spectral interpolation where pixels used for the restoration are spectrally distant and spatially close. The spectral inpainting method described above enables a robust estimation of missing lines as it is only based on spectral information. As illustrated in figures 5.5, 5.6 and 5.7 restoration with spectral inpainting provides images visually identical to the original band 6, and unlike global and local interpolation does not display any stripes. Scatter plots (figure ) and quantitative analysis reported in table indicate reliable results obtained with the spectral inpainting for all three images of Alaska, Labrador and Siberia. 121
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École Doctorale d’Informatique,
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5 Résumé Nou abordons dans cette
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8 TABLE DES MATIÈRES 3.5 Frequency
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10 TABLE DES MATIÈRES
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12 1. Introduction A common issue f
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14 1. Introduction
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16 2. Remote Sensing with MODIS In
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38 2. Remote Sensing with MODIS
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40 3. Standard destriping technique
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Page 134 and 135: 134 BIBLIOGRAPHIE P. Perona and J.
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