Titre :	Etudes comparatives de quelques algorithmes d’imagerie
Type de document :	document électronique
Auteurs :	Soulef Bougueroua, Auteur ; Nourreddine Daili, Directeur de thèse
Editeur :	Setif:UFA
Année de publication :	2024
Importance :	1 vol (99 f .)
Format :	29 cm
Langues :	Français (fre)
Catégories :	Thèses & Mémoires:Mathématique
Mots-clés :	Algorithms  Application  Image restoration comparative study  Restoration models  Image processing Etude comparatives de restauration d'image  Modèles de restauration  Traitement d'images
Index. décimale :	510 Mathématique
Résumé :	Inverse problems are too broad a field. Among the inverse problems in which I am interested in image processing in my work. Image restoration is a problem that is ill-posed, interesting and of crucial importance to the notion of image processing. The noise damages images, which is why several algorithms have been developed for processing images: the regularization of Tychonov ; the Rudin-Osher-Fatemi continuous model ; the Model of Yves Meyer ; the Osher-Solé-Vese model ; the Gheraibia-Daili model ; ... In this thesis, we treated the restoration models cited above; we did comparative studies by making theoretical and numerical implementations. We studied the Bregman projection theorem and oblique projection. We present a new optimization method to solve the problems of restoring images disturbed by additive white Gaussian noise. This resolution method is based on an algorithm of prox-penalty. The numerical results obtained by the prox-penalty method, the algorithm split Bregman for anisotropic and isotropic TV denoising problems in terms of image quality, convergence and signal noise ratio (SNR), these are compared in my thesis
Note de contenu :	Tabledesmatieres 0.1 IntroductionGenerale . .............................4 0.1.1 L'Histoire duTraitementd'Image . .................4 0.1.2 Domaines d'ApplicationsduTraitementd'Image . .......7 0.1.3 Algorithmes d'Imagerie . ........................8 0.1.4 L'ObjectifetleContenuduMemoire . ...............8 1 Generalites10 1.1 Elementsdelatheoried'AnalyseFonctionnelle . .............10 1.1.1 OperateurLineareBorne . .......................11 1.1.2 Le SpectreetResolvanted'unOperateur . ............12 1.2 GeneralitessurlesEspacesdeSobolev . ..................12 1.3 Optimisation danslesEspacesdeBanach . ................13 1.3.1 Semi-continuiteetConvexitedeFonctionnellessurV . .....14 1.3.2 G^ateaux-DierentiabilitedesFonctionnellesConvexes . ....14 1.3.3 Minimisation dansunBanachRe exif . ..............15 1.3.4 Les Projections . .............................15 1.4 ProblemeInverseetProblemeMalPose . .................18 1.5 TraitementNumeriquedesImages . .....................18 1.5.1 Les ImagesNumerique . ........................18 1.5.2 L'Imagerie Medicale . ..........................20 1.6 Des Mesures . ...................................21 1.6.1 Erreur quadratiquemoyenne . ....................21 1.6.2 Rapportsignal/bruitdecr^ete . ....................21 1.6.3 Erreur absoluenormalisee . ......................21 1.6.4 Dierencemoyenne . ..........................21 1.6.5 Dierencemaximale . ..........................22 1.6.6 Correlationcroiseenormalisee . ...................22 1.6.7 Contenustructurel . ...........................22 2 LaMethodedeRegularisationdeTychonov24 2.1 IntroductionHistorique . ............................24 2.2 RegularisationLineaire(Tykhonov) . ....................25 2.2.1 La MethodedeTykhonovenEDP . .................26 2.3 La MethodedeTykhonovGeneralise . ...................27 2.3.1 Deux MethodesdeTikhonovGeneralisees . ............28 2.4 La MethodedeTykhonovenImagerie . ..................31 2.4.1 ResultatsNumeriquespourleModeledeTykhonov . .....33 2.5 Conclusions . ...................................33 3 ModeledeRudin-Osher-Fatemi38 3.1 IntroductionHistorique . ............................38 3.2 ProblemedeROF . ...............................39 3.2.1 Discretisation . ..............................43 3.2.2 Image Debruitee . ............................45 3.3 ResultatsNumeriques . .............................45 3.4 Conclusions . ...................................46 4 ModeledeYvesMeyeretVeseOsher51 4.1 Introduction . ...................................51 4.2 ProblemedeMeyer . ..............................52 4.2.1 La relationentreROFetMeyer . ..................53 4.2.2 DiscretisationduModeledeMeyer . ................54 4.3 ProblemedeVeseOsher . ...........................55 4.3.1 DiscretisationNumeriqueduModeledeMeyer . .........55 4.3.2 ResolutionduProblemedeVeseOsher . ..............57 5 TheoremesdeProjectiondeBregmanetProjectionOblique59 5.1 IntroductionHistorique . ............................59 5.2 TheoremedeProjectiondeBregman . ...................60 5.2.1 Distance deBregman . .........................61 5.3 TheoremedeProjectionOblique . .....................64 5.3.1 Introductionauprojectionoblique . .................64 5.3.2 ProjectionOblique . ...........................65 5.3.3 Projectionobliqueiterativesurdesensemblesconvexetproblemes de faisabilitedivisee(SFP) . .....................67 5.3.4 Problemes(SFP)etl'algorithmeCQ . ...............67 5.3.5 Convergencedel'algorithmeCQ . ..................69 5.3.6 Les methodesLandweber . ......................70 5.3.7 Le CFPetl'algorithmeMSFP . ...................70 5.4 Algorithmes IterativedeBregman . .....................71 5.4.1 TheoremedeConvergence . ......................73 6 AnalysesComparativesdesAlgorithmesdeProximalePenaliteetdeBreg- man pourleDebruitageD'image74 6.1 MethodesProximale-Penalite . ........................74 6.2 Algorithmes deBregmanetImagerie . ...................77 6.2.1 Algorithme deSplitBregman . ...................77 6.2.2 ProblemedeDebruitageTVAnisotrope . .............78 6.2.3 ProblemedeDebruitageTVIsotrope . ...............79 6.2.4 CombinaisondesProblemesDebruitageTVAnisotropeet Isotrope . .................................79 6.2.5 TheoremedeConvergence . ......................80 6.3 ResultatsNumeriques . .............................83 6.4 Conclusion . ....................................91 Bibliographie
Côte titre :	dm/0200
En ligne :	https://drive.google.com/file/d/1gTaCb6QO4nVMzIqS3OHA_GUT4xW-up6P/view?usp=shari [...]
Format de la ressource électronique :	pdf

Etudes comparatives de quelques algorithmes d’imagerie [document électronique] / Soulef Bougueroua, Auteur ; Nourreddine Daili, Directeur de thèse . - [S.l.] : Setif:UFA, 2024 . - 1 vol (99 f .) ; 29 cm.
Langues : Français (fre)

Catégories :	Thèses & Mémoires:Mathématique
Mots-clés :	Algorithms  Application  Image restoration comparative study  Restoration models  Image processing Etude comparatives de restauration d'image  Modèles de restauration  Traitement d'images
Index. décimale :	510 Mathématique
Résumé :	Inverse problems are too broad a field. Among the inverse problems in which I am interested in image processing in my work. Image restoration is a problem that is ill-posed, interesting and of crucial importance to the notion of image processing. The noise damages images, which is why several algorithms have been developed for processing images: the regularization of Tychonov ; the Rudin-Osher-Fatemi continuous model ; the Model of Yves Meyer ; the Osher-Solé-Vese model ; the Gheraibia-Daili model ; ... In this thesis, we treated the restoration models cited above; we did comparative studies by making theoretical and numerical implementations. We studied the Bregman projection theorem and oblique projection. We present a new optimization method to solve the problems of restoring images disturbed by additive white Gaussian noise. This resolution method is based on an algorithm of prox-penalty. The numerical results obtained by the prox-penalty method, the algorithm split Bregman for anisotropic and isotropic TV denoising problems in terms of image quality, convergence and signal noise ratio (SNR), these are compared in my thesis
Note de contenu :	Tabledesmatieres 0.1 IntroductionGenerale . .............................4 0.1.1 L'Histoire duTraitementd'Image . .................4 0.1.2 Domaines d'ApplicationsduTraitementd'Image . .......7 0.1.3 Algorithmes d'Imagerie . ........................8 0.1.4 L'ObjectifetleContenuduMemoire . ...............8 1 Generalites10 1.1 Elementsdelatheoried'AnalyseFonctionnelle . .............10 1.1.1 OperateurLineareBorne . .......................11 1.1.2 Le SpectreetResolvanted'unOperateur . ............12 1.2 GeneralitessurlesEspacesdeSobolev . ..................12 1.3 Optimisation danslesEspacesdeBanach . ................13 1.3.1 Semi-continuiteetConvexitedeFonctionnellessurV . .....14 1.3.2 G^ateaux-DierentiabilitedesFonctionnellesConvexes . ....14 1.3.3 Minimisation dansunBanachRe exif . ..............15 1.3.4 Les Projections . .............................15 1.4 ProblemeInverseetProblemeMalPose . .................18 1.5 TraitementNumeriquedesImages . .....................18 1.5.1 Les ImagesNumerique . ........................18 1.5.2 L'Imagerie Medicale . ..........................20 1.6 Des Mesures . ...................................21 1.6.1 Erreur quadratiquemoyenne . ....................21 1.6.2 Rapportsignal/bruitdecr^ete . ....................21 1.6.3 Erreur absoluenormalisee . ......................21 1.6.4 Dierencemoyenne . ..........................21 1.6.5 Dierencemaximale . ..........................22 1.6.6 Correlationcroiseenormalisee . ...................22 1.6.7 Contenustructurel . ...........................22 2 LaMethodedeRegularisationdeTychonov24 2.1 IntroductionHistorique . ............................24 2.2 RegularisationLineaire(Tykhonov) . ....................25 2.2.1 La MethodedeTykhonovenEDP . .................26 2.3 La MethodedeTykhonovGeneralise . ...................27 2.3.1 Deux MethodesdeTikhonovGeneralisees . ............28 2.4 La MethodedeTykhonovenImagerie . ..................31 2.4.1 ResultatsNumeriquespourleModeledeTykhonov . .....33 2.5 Conclusions . ...................................33 3 ModeledeRudin-Osher-Fatemi38 3.1 IntroductionHistorique . ............................38 3.2 ProblemedeROF . ...............................39 3.2.1 Discretisation . ..............................43 3.2.2 Image Debruitee . ............................45 3.3 ResultatsNumeriques . .............................45 3.4 Conclusions . ...................................46 4 ModeledeYvesMeyeretVeseOsher51 4.1 Introduction . ...................................51 4.2 ProblemedeMeyer . ..............................52 4.2.1 La relationentreROFetMeyer . ..................53 4.2.2 DiscretisationduModeledeMeyer . ................54 4.3 ProblemedeVeseOsher . ...........................55 4.3.1 DiscretisationNumeriqueduModeledeMeyer . .........55 4.3.2 ResolutionduProblemedeVeseOsher . ..............57 5 TheoremesdeProjectiondeBregmanetProjectionOblique59 5.1 IntroductionHistorique . ............................59 5.2 TheoremedeProjectiondeBregman . ...................60 5.2.1 Distance deBregman . .........................61 5.3 TheoremedeProjectionOblique . .....................64 5.3.1 Introductionauprojectionoblique . .................64 5.3.2 ProjectionOblique . ...........................65 5.3.3 Projectionobliqueiterativesurdesensemblesconvexetproblemes de faisabilitedivisee(SFP) . .....................67 5.3.4 Problemes(SFP)etl'algorithmeCQ . ...............67 5.3.5 Convergencedel'algorithmeCQ . ..................69 5.3.6 Les methodesLandweber . ......................70 5.3.7 Le CFPetl'algorithmeMSFP . ...................70 5.4 Algorithmes IterativedeBregman . .....................71 5.4.1 TheoremedeConvergence . ......................73 6 AnalysesComparativesdesAlgorithmesdeProximalePenaliteetdeBreg- man pourleDebruitageD'image74 6.1 MethodesProximale-Penalite . ........................74 6.2 Algorithmes deBregmanetImagerie . ...................77 6.2.1 Algorithme deSplitBregman . ...................77 6.2.2 ProblemedeDebruitageTVAnisotrope . .............78 6.2.3 ProblemedeDebruitageTVIsotrope . ...............79 6.2.4 CombinaisondesProblemesDebruitageTVAnisotropeet Isotrope . .................................79 6.2.5 TheoremedeConvergence . ......................80 6.3 ResultatsNumeriques . .............................83 6.4 Conclusion . ....................................91 Bibliographie
Côte titre :	dm/0200
En ligne :	https://drive.google.com/file/d/1gTaCb6QO4nVMzIqS3OHA_GUT4xW-up6P/view?usp=shari [...]
Format de la ressource électronique :	pdf