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8 TABLE DES MATIÈRES 3.5 Frequency filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.5.1 Spectral Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.5.2 Band-pass filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.6 Haralick Facet filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.7 Multiresolution approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.7.1 Limitations of fourier transform . . . . . . . . . . . . . . . . . . . . . 57 3.7.2 Multiresolution analysis . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.7.3 Wavelet basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.7.4 Filter banks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.7.5 2D wavelet basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.7.6 Destriping with wavelet coefficient thresholding . . . . . . . . . . . . 62 3.8 Assessing destriping quality . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.8.1 Noise Reduction Ratio and Image Distortion . . . . . . . . . . . . . 65 3.8.2 Radiometric Improvement Factors . . . . . . . . . . . . . . . . . . . 66 3.8.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4 A Variational approach for the destriping issue 73 4.1 PDEs and variational methods in image processing . . . . . . . . . . . . . . 73 4.2 Rudin, Osher and Fatemi Model . . . . . . . . . . . . . . . . . . . . . . . . 76 4.3 Striping as a texture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.3.1 Yves Meyer’s model for oscillatory functions . . . . . . . . . . . . . . 83 4.3.2 Vese-Osher’s Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.3.3 Osher-Solé-Vese’s Model . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.3.4 Other u + v models . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4.3.5 Experimental results and discussion . . . . . . . . . . . . . . . . . . 88 4.4 Destriping via gradient field integration . . . . . . . . . . . . . . . . . . . . 91 4.5 A unidirectional variational destriping model . . . . . . . . . . . . . . . . . 94 4.6 Optimal regularization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 4.6.1 Tadmor-Nezzar-Vese (TNV) hierarchical decomposition . . . . . . . 99 4.6.2 Osher et al. iterative regularization method . . . . . . . . . . . . . . 100 4.6.3 Stopping criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 4.6.4 Experimental results and discussion . . . . . . . . . . . . . . . . . . 103 5 Application : Restoration of Aqua MODIS Band 6 111 5.1 Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 5.2 Existing restoration techniques . . . . . . . . . . . . . . . . . . . . . . . . . 113 5.2.1 Global interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 5.2.2 Local interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 5.3 Proposed approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 5.3.1 Spectral similarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 5.3.1.1 Spectral Correlation Measure . . . . . . . . . . . . . . . . . 115 5.3.1.2 Spectral Angle Measure . . . . . . . . . . . . . . . . . . . . 116
9 5.3.1.3 Euclidian Distance Measure . . . . . . . . . . . . . . . . . . 116 5.3.1.4 Spectral Information Divergence Measure . . . . . . . . . . 116 5.3.2 Spectral inpainting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 5.4 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 5.4.1 Validation of spectral inpainting using NDSI measurements . . . . . 119 5.4.2 Assessing the impact of stripe noise . . . . . . . . . . . . . . . . . . 122 Conclusion 126 Bibliographie 135
Page 1: École Doctorale d’Informatique,
Page 5: 5 Résumé Nou abordons dans cette
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Page 12 and 13: 12 1. Introduction A common issue f
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- Alaska Labrador Siberia Restorati
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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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