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54 3. Standard destriping techniques and application to MODIS Figure 3.12 – (Left) Original image from Terra MODIS band 27 (Right) Image destriped with the filter H 1 components. This results in high-pass filtered images containing mostly stripe noise. In addition, the mean value of filtered images differs from the original signal. To overcome this issue, we consider the following low-pass filter : H B (u, v) =exp (− u2 + v 2 ) σ 2 B (3.18) where σ B is small enough so that the filter H B mainly retrieves the mean value of the noisy image. The destriped image is then obtained with the filter : H 2 (u, v) =H 1 (u, v)+H B (u, v) (3.19) An alternative implementation of the FIR filter can be done in the spatial domain by convolving each column with a unidimensional spatial FIR filter kernel derived from the Parks-McClellan (PM) algorithm [Parks and Mcclellan, 1972]. Destriping in the spatial domain overcomes many limitations compared to the 2D fourier filtering. It removes the constraints related to images dimensions being a power of two and slightly reduces horizontal edge effects. Another FIR filtering approach was presented in [Srinivasan et al., 1988] for the destriping of Landsat. The fourier response of the proposed filter is composed of concentric rings centered at stripe frequencies. This method however, smoothes data equally in both directions and introduces blurring and ringing artefacts along the discontinuities of the images.
55 Image distortion ID 1 0.98 0.96 0.94 0.92 0.9 0.88 0.86 0.84 0 0 10 20 30 40 50 σ ID NR 2000 1600 1200 800 400 Noise reduction NR Image distortion ID 1 0.98 0.96 0.94 0.92 0.9 0.88 0.86 0.84 ID NR 30 25 20 15 10 0 0 10 20 30 40 50 σ 5 Noise reduction NR Figure 3.13 – ID and NR indexes as a function of σ in the filter H 2 for images of (Left) Terra band 27 and (Right) Terra band 30. The value of σ B is fixed to 5. Images from band 27 are representative of smooth atmospheric effects and therefore, small scale structures in the images are mostly due to striping. In (Left) for σ > 21, the filter H 2 behaves as a high-pass filter that retains only high-frequency components, coincident with stripe noise, hence the decrease in NR. This effect is not visible on images from band 30 where high-frequencies are composed of land-ocean-clouds discontinuities. 3.6 Haralick Facet filtering Destriping techniques described this far are only dedicated to only periodic stripes and fail to process random stripes. Application on images extracted from Terra MODIS band 33 do not display any improvement (and therefore are not illustrated). The study presented in [Rakwatin et al., 2007] was the first to tackle the issue of random stripes on MODIS. Rakwatin proposed an hybrid approach that combines histogram matching for the removal of detector-to-detector stripes and mirror banding, with an iterated weighted least squares facet filtering for random stripes. The facet model introduced in [Haralick and Watson, 1981] decomposes a given image into connected facets. A given pixel is contained in K 2 different blocks each composed of K × K pixels. For a pixel i, we denote W i,k a resolution cellcomposed of k = {1, .., K × K} neighbooring pixels. A given pixel is contained in several resolution cells as they overlap with each other. Let us denote by J ik (r, c) the signal value at row r and column c in the resolution cell W ik . Haralick’s sloped facet model assumes that J ik (r, c) can be expressed as : J ik (r, c) =α ik r + β ik c + γ ik + n ik (r, c) (3.20) where α ik , β ik and γ ik represent the slope plan coefficients of the facet model in the cell W ik and n ik is the noise. Denoting (−L, −L) (resp. (L, L)) the relative row-column coordinates of a cell upper-left corner (resp. lower-right corner), the values of a resolution cell slope plane coefficients can be estimated by minimizing the following quadratic energy
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École Doctorale d’Informatique,
Page 5: 5 Résumé Nou abordons dans cette
Page 8 and 9: 8 TABLE DES MATIÈRES 3.5 Frequency
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112 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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