Critère de qualité d'une image: RMS max ( Root Mean Square ou Standard Deviation ) 4 possibilités de filtrage "ondelettes": programmes existent 1. ondelette de Haar ( continue, mais pas assez régulière ) 2. " " " " " " " " " + "cyclic averaging" sur 1 seul niveau 3. ondelette daub4 de Daubechies ( plus régulière; 2 moments nuls ) 4. " " " " " " " " " + "cyclic averaging" sur 1 seul niveau Rmq. Utiliser les 2. et 4. pour supprimer les eventuelles oscillations, crées par le seuillage, autour des singularités: see pages 450-452 (Translation Invariance) in the book of Stéphane Mallat "Wavelet Tour of Signal Processing", Academic Press, 1998 Rmq. "Cyclic averaging" is a technique of "cycle-spinning" proposed by Coifman and Donoho for noise removal: see pages 445-446 (Translation Invariant Thresholding) in the book of Stéphane Mallat "Wavelet Tour of Signal Processing", Academic Press, 1998 a. La meilleure image (8): RMS = 77.4029 b. L'image moyenne: RMS = 76.4046 calcul de a. et b. par le programme: cmoments.pro Computing of Mean, Variance, Mean Absolute Deviation, Standard Deviation Format conversion from .bin to .gif for 15 images of spicules and for average image Data: Image 0 Image 1 Image 2 Image 3 Image 4 Image 5 Image 6 Image 7 Image 8 Image 9 Image 10 Image 11 Image 12 Image 13 Image 14 Results: Average Image Mean,Variance,Mean Absolute Deviation,Standard Deviation c. La meilleure image après filtrage par seuillage "ondelettes": 1. filtre de Haar + "cyclic averaging" la meilleur image filtrée (11): RMS= 88.4492 calcul (seuil p = 7.;trouver le seuil optimal!) par le programme: spin.pro Denoising by cyclic averaging of wavelet thresholding using Haar filter within a loop of 15 images of spicules Computing the average denoised image Write all denoised images in gif format Results:Denoised Image 0 Denoised Image 1 Denoised Image 2 Denoised Image 3 Denoised Image 4 Denoised Image 5 Denoised Image 6 Denoised Image 7 Denoised Image 8 Denoised Image 9 Denoised Image 10 Denoised Image 11 Denoised Image 12 Denoised Image 13 Denoised Image 14 Average Denoised Image Mean,Variance,Mean Absolute Deviation,Standard Deviation 2. filtre "daub4" + "cyclic averaging" la meilleur image filtrée (11): RMS= 89.9770 calcul (seuil p = 7.;trouver le seuil optimal!) par le programme: spindaub.pro Denoising by Daub4 wavelet thresholding and cyclic averaging within a loop of 15 images of spicules Computing the average denoised image Write all denoised images in gif format Results:Denoised Image 0 Denoised Image 1 Denoised Image 2 Denoised Image 3 Denoised Image 4 Denoised Image 5 Denoised Image 6 Denoised Image 7 Denoised Image 8 Denoised Image 9 Denoised Image 10 Denoised Image 11 Denoised Image 12 Denoised Image 13 Denoised Image 14 Average Denoised Image Mean,Variance,Mean Absolute Deviation,Standard Deviation d. L'image moyenne en utilisant les images filtrés par seuillage "ondelettes": 1. filtre de Haar + "cyclic averaging" l'image moyenne: RMS = 86.3804 calcul (seuil p = 7.;trouver le seuil optimal!) par le programme: spin.pro (voir ci-dessus) 2. filtre "daub4" + "cyclic averaging" l'image moyenne: RMS = 87.4258 calcul (seuil p = 7.;trouver le seuil optimal!) par le programme spindaub.pro (voir ci-dessus) e. L'image reconstruite sur séquence non filtrée: l'image reconstruite: RMS = 78.018 moments calcul par le programme: maxpows.pro Function to reconstruct best image using power maximization in Fourier domain for 15 images of spicules Computing Mean,Variance,Mean Absolute Deviation,Standard Deviation of 'maxpow' image Saving reconstructed image in gif format Version with minimized virtual memory Results:Reconstructed Image Mean,Variance,Mean Absolute Deviation,Standard Deviation f. L'image reconstruite sur séquence filtrée: 1. filtre de Haar + "cyclic averaging" pour chacune des 15 images l'image reconstruite: RMS = 89.6376 moments calcul (seuil p = 7.;trouver le seuil optimal!) par les programmes: maxpowspinh.pro Function to reconstruct best image using power maximization in Fourier domain for 15 images of spicules; each image is denoised by Haar wavelet thresholding and cyclic averaging Version with minimized virtual memory Results:Reconstructed Image Mean,Variance,Mean Absolute Deviation,Standard Deviation denoisec.pro Denoising by wavelet thresholding using Haar filter and cyclic averaging ( image as an array - parameter ) 2. filtre "daub4" + "cyclic averaging" pour chacune des 15 images l'image reconstruite: RMS = 90.5381 moments calcul (seuil p = 7.;trouver le seuil optimal!) par les programmes: maxpowspind.pro Function to reconstruct best image using power maximization in Fourier domain for 15 images of spicules; each image is denoised by daub4 wavelet thresholding and cyclic averaging Version with minimized virtual memory Results:Reconstructed Image Mean,Variance,Mean Absolute Deviation,Standard Deviation denoises.pro Denoising by Daub4 wavelet thresholding and cyclic averaging ( image as an array - parameter ) Estimation du seuil p: 1. en utilisant HISTOGRAM: 2. en utilisant MEDIAN: estim1.pro Noise variance and threshold estimation using MEDIAN for 15 images of spicules ( see page 447 (Noise Variance Estimation) in the book of Stéphane Mallat "Wavelet Tour of Signal Processing", Academic Press, 1998 ) Results:Noise variance and threshold Autre critère de "qualité" => grad max au limbe coupe dans les spicules, orthogonalement et en intégrant sur quelques pixels Programme de recentrage écrit par Clive Fong à mettre dans public_html/debruitage Suggestions pour améliorer MFM? Temps de calcul pour 1 passage avec 15 images et 512 x 512 ? Plusieurs passages pour améliorer le rapport Signal/Bruit et utiliser 2 autres déterminations. Mise à jour : le 5 novembre 1998. Fichier source: http://www.ann.jussieu.fr/~koutchmy/debruitage/spicul~2.html ou ~/ondelettes/wavelets/spicul~2.html
