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Table 3.4 – Noise Reduction (NR), Image distortion (ID), radiometric Improvement Factors IF 1 and IF 2 for the Terra MODIS band 27, 30 and 33 – Terra band 27 Terra band 30 Terra band 33 index NR ID IF 1 IF 2 NR ID IF 1 IF 2 NR ID IF 1 IF 2 moment matching 45.8895 0.6305 7.3085 11.5732 9.4280 0.9963 6.2656 6.6818 – 0.9995 0.1637 0.1724 histogram (IMAPP) 101.0629 0.9459 8.5463 20.1003 15.3316 0.8816 5.7455 12.8977 – 0.9773 4.8320 11.1566 IFOV 100.5751 0.9692 5.8563 13.7338 5.4195 0.8991 4.6190 5.7684 – 0.9388 -0.1046 0.5466 Frequency filtering 1784 0.9868 9.8866 21.5316 25.5615 0.9884 7.3092 14.8566 – – – – Wavelet thresholding 5749 0.9326 9.8649 38.3728 48.9917 0.9050 6.2421 18.6632 – 0.8892 4.7349 17.0134 Table 3.5 – Noise Reduction (NR), Image distortion (ID), radiometric Improvement Factors IF 1 and IF 2 for the Aqua MODIS band 27, 30 and 36 – Aqua band 27 Aqua band 30 Aqua band 36 index NR ID IF 1 IF 2 NR ID IF 1 IF 2 NR ID IF 1 IF 2 moment matching 12.643 0.984 10.4393 12.0686 4.2363 0.9991 6.4180 12.6573 1.90 0.9997 3.1844 2.3252 histogram (IMAPP) 33.8517 0.9828 11.5966 18.1798 4.4847 0.9839 5.5991 12.6135 1.9593 0.9957 3.2537 2.4242 IFOV 1 12.1310 0.9890 9.3335 11.9212 1.8756 0.9646 -3.6762 8.9016 1.1396 0.8627 -1.8263 2.3097 frequency filtering 510.5828 0.9854 10.3039 24.8529 7.8478 0.9874 6.35 17.8977 3.2048 0.9868 0.7912 10.6393 wavelet thresholding 1131 0.9280 9.6601 25.4008 13.4574 0.9288 6.1015 17.9192 5.2528 0.8918 -0.1918 11.3379 72 3. Standard destriping techniques and application to MODIS
73 Chapitre 4 A Variational approach for the destriping issue 4.1 PDEs and variational methods in image processing Many disciplines from physical sciences such as thermodynamics and fluids mechanics have inspired the application of Partial Differential Equations (PDEs) in the field of image processing. Early denoising methods are mostly based on smoothing operations, either computed directly in the spatial domain via a convolution with a filter, or in the frequency domain. Assuming the noise to be contained in the high frequencies of the observed signal, a common restoration technique consists in convolving the noisy image with a linear operator. Denoting u 0 the noisy signal defined in a bounded domain Ω of R 2 , an estimate of the true image u is obtained by considering the scale-space generated by u 0 as : ∫ u(x, y, t) = G(x − ξ, y − η, t)u 0 (ξ, η)dxdy, (x, y) ∈ Ω (4.1) Ω Typically, the operator G is a bidimensional gaussian kernel : G(x, y, t) = 1 ( −(x 2 4πt exp + y 2 ) ) 4t (4.2) where the variance σ 2 =2t of the gaussian operator controls the degree of smoothing in the restored image u. The work of [Koenderink, 1984] reformulates the convolution with a gaussian kernel as a diffusion process where the value of a pixel can be expressed with respect to a neighboorhood which size is determined by the variance σ 2 of the operator G. The noise free image u can be seen as the solution of a simple parabolic PDE : ∂u ∂t (x, y, t) u =∂2 ∂ 2 x (x, y, u t)+∂2 ∂ 2 (x, y, t) y u(x, y, 0) = u 0 (x, y) (4.3)
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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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18 2. Remote Sensing with MODIS Fig
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20 2. Remote Sensing with MODIS Fig
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- Alaska Labrador Siberia Restorati
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126 5. Application : Restoration of
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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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