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114 5. Application : Restoration of Aqua MODIS Band 6 missing data over vegetation, clouds, desert or oceanic surfaces require further refinement to distinguish surface cover types. In addition, it is assumed that the polynomial relation established on Terra data is transposable to Aqua. This assumption is all the more sensitive to unknown calibration differences between Terra and Aqua MODIS, and the striping noise described in the previous chapters. Furthermore, the analytical relation is derived without prior pre-processing of bands 7 and 6 for stripe noise removal. 5.2.2 Local interpolation More recently, Rakwatin2009 proposed a restoration procedure for Aqua MODIS band 6 that consists in three step :1) the determination of non functioning detectors ; 2) the correction of periodic stripes for functioning detectors using histogram matching ; 3) the estimation of missing pixels via local cubic polynomial regression between band 6 and band 7. Similarly to the approach proposed in [L. L. Wang and Nianzeng], the high correlation between band 6 and 7 reflectances is quantified using polynomial regression. However, the fitting is computed locally to account for land cover types. The restoring algorithm can be summarized with the following : 1) For a dead pixel x in band 6, a initial rectangular window of size 15 × 3 is centered at x. The minimum and maximum values of the window in band 7, respectively ρ min 7 and ρ max 7 and their location x min , x max are determined. 2) If ρ min 7 ≤ ρ 7 (x) ≤ ρ max 7 , a local cubic polynomial function is calculated from the values ρ 7 (x min ), ρ 7 (x max ), ρ 6 (x min ) and ρ 6 (x max ) and used to estimated the values of ρ 6 (x) 3) If ρ 7 (x) < ρ min 7 , ρ 7 (x) > ρ max 7 or if pixels x min or x max in band 6 are also dead, the size of the analizing window is increased until these criteria are met. 4) Step 1, 2 and 3 are repeated for every dead pixel of band 6 This local cubic interpolation procedure is illustrateed in figure 5.3. 5.3 Proposed approach We propose here a simple methodology to estimate the value of Aqua MODIS band 6 missing pixels. The approach is based on a concept widely used in the field of hyperspectral image classification, spectral similarity. Data collected from MODIS can be perceived as a cube, where the third dimension represents the signal’s wavelenght and can also be used to extract useful information. In hyperspectral remote sensing, the determination of surface composition requires the analysis of its reflectance spectrum and comparison with known field spectra via spectral matching techniques [Kruse et al.]. Although conditionned by the number of available spectral bands, this reasoning also applies to multispectral imagery.
115 ρ 6 (x max ) MODIS Band 6 ρ 6 (x) ρ 6 (x min ) ρ 7 min ρ 7 (x) MODIS Band 7 ρ 7 max Figure 5.3 – Restoration procedure for Aqua MODIS band 6 proposed in (Rakwatin et al., 2009) and based on a local cubic interpolation For the issue of Aqua MODIS band 6 restoration, missing pixels can be estimated using spectrally similar pixels from functionning detectors. To this purpose, let us first recall the definition of few spectral similarity measures commonly used in hyperspectral image classification. 5.3.1 Spectral similarity We denote by ρ(x) the reflectance of a given pixel x, which we consider as a vector in a n-dimensional space as : ρ(x) =(ρ 1 (x),ρ 2 (x), ..., ρ n (x)) T (5.4) Each component of the vector ρ(x) in (5.4) corresponds to the reflectance of pixel x in a given spectral band. 5.3.1.1 Spectral Correlation Measure The Spectral Correlation Measure (SCM) was defined in [der Meero and Bakker] and is computed for two pixels x and y as : n ∑ n 1 SCM(x, y) = ρ(x)ρ(y) − ∑ n 1 ρ(x) ∑ n √ 1 ∑ ρ(y) [n n 1 ρ(x)2 − ( ∑ n 1 ρ(x))2 ][n ∑ n 1 ρ(y)2 − ( ∑ n (5.5) 1 ρ(y))2 ] where n is the number of overlapping spectral bands. The SCM measures the correlation between the two vectors ρ(x) and ρ(y) and takes into account the mean value and variance of the overall spectral shape. The values of SCM are contained in the interval [-1,1].
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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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