University Sétif 1 FERHAT ABBAS Faculty of Sciences
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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'imagesIndex. 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 thesisNote 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-Di erentiabilitedesFonctionnellesConvexes . ....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 Di erencemoyenne . ..........................21
1.6.5 Di erencemaximale . ..........................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
BibliographieCôte titre : dm/0200 En ligne : https://drive.google.com/file/d/1gTaCb6QO4nVMzIqS3OHA_GUT4xW-up6P/view?usp=shari [...] Format de la ressource électronique : 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'imagesIndex. 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 thesisNote 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-Di erentiabilitedesFonctionnellesConvexes . ....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 Di erencemoyenne . ..........................21
1.6.5 Di erencemaximale . ..........................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
BibliographieCôte titre : dm/0200 En ligne : https://drive.google.com/file/d/1gTaCb6QO4nVMzIqS3OHA_GUT4xW-up6P/view?usp=shari [...] Format de la ressource électronique : Exemplaires (1)
Code-barres Cote Support Localisation Section Disponibilité DM/0200 DM/0200 Thèse Bibliothéque des sciences Français Disponible
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