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64 3. Standard destriping techniques and application to MODIS Figure 3.16 – (Left) Noisy image from Terra MODIS band 30 (Right) Destriped result setting to zero vertical details d 1 1 , d1 2 and d1 3 (m=3) prior to wavelet reconstruction Image distortion ID 0.93 0.925 0.92 0.915 0.91 0.905 0.9 0.895 0.89 0.885 0.88 ID NR 7000 6000 5000 4000 3000 2000 1 2 3 4 5 6 7 8 0 1000 m (db2) Noise reduction NR Image distortion ID 0.935 0.93 0.925 0.92 0.915 0.91 0.905 ID NR 7000 6000 5000 4000 3000 2000 0.9 1000 0.895 1 2 3 4 5 6 7 8 0 m (db4) Noise reduction NR Figure 3.17 – Image distortion (ID)* and Noise reduction (NR)* as a function of the thresholding parameter m for Terra MODIS band 27. The selected wavelets are (Left) db2 and (Right) db4. The breaking points visible in the NR curves at m = 5 for the wavelet db 2 and m = 3 for db 4 , translate the reduction of striping from higher to lower resolution scales. Depending on the number of vanishing moments of the selected wavelet, the striping will be concentrated in the wavelet coefficients of higher resolutions and its impact on vertical wavelet coefficients eventually fades below at given scale, hence the constant NR in lower resolutions. visible. This is due to non-linear effects and random stripes, mostly present on Terra MO- DIS. Despite uncomplete destriping, equalization techniques are often prefered for their ability to preserve the signal radiometry. On the other hand, filtering methods (frequency filtering, facet filtering and wavelet thre-
65 sholding) can be tuned to regulate the amount of distortion introduced in the restored image. A rigourous comparison of these methods requires additional criteria other than visual interpretation. In this section, we recall the definition of several qualitative indexes used to evaluate the destriping quality. 3.8.1 Noise Reduction Ratio and Image Distortion The spectral analysis conducted in section 3.5.1, takes advantage of the unidirectional aspect of striping to highlight its spectral signature. Periodic stripes related to detectorto-detector and mirror banding introduces peaks, clearly visible in the ensemble averaged power spectrum down the columns. A reliable destriping should reduce the stripe peaks without interfering with the global shape of the original signal’s power spectrum. Let us denote P 0 -resp. P 1 - the power spectrum obtained as an average of the periodograms of the noisy image -resp. the destriped image- columns. We define : N 0 = ∑ P 0 (f) f∈BW N N 1 = ∑ P 1 (f) f∈BW N (3.52) where BW N is the noisy part of the frequency spectrum (f ∈ BW N corresponds to f ∈ {0.1, 0.2, 0.3, 0.4, 0.5} in the case of detector-to-detector stripes). N 0 and N 1 contain the spectral components of stripes in both the noisy image and the restored one. The Noise Reduction ratio (NR) is then defined as : NR = N 0 N 1 (3.53) The NR index measures the attenuation of the frequency peaks in the power spectrum and hence can only be used for images affected with periodic stripes. Furthermore, evaluation of a destriping techniques with the NR index has to be imperatively completed with a distortion index that quantifies the blur introduced in the destriped result. Denoting : S 0 = ∑ P 0 (f) f∈BW S S 1 = ∑ P 1 (f) f∈BW S (3.54) where BW S is the noise-free portion of the spectrum, the image distortion index used in [Pan and Chang, 1992] is defined as : ID = N 0 N 1 (3.55)
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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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114 5. Application : Restoration of
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- Alaska Labrador Siberia Restorati
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128 Conclusion
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130 BIBLIOGRAPHIE A. Chambolle. An
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132 BIBLIOGRAPHIE E. Hochberg, S. A
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134 BIBLIOGRAPHIE P. Perona and J.
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