Restauration des images naturelles et préservation de la texture à l'aide de noyaux de taille normale.

Accueil || Parcours || Recherche || S'enregistrer || Mon Compte || Contacts || Aide || Langues

Azzabou, Noura (2008) Restauration des images naturelles et préservation de la texture à l'aide de noyaux de taille normale. Doctorat, ENPC p.199.

Plein texte disponible en tant que : - ThesisNouraAzzabou.pdf ( 23313 Kb )

Licence: Copyright

Résumé

Cette thèse s’intéresse aux problèmes de restauration d’images et de préservation de textures. Cette tache nécessite un modèle image qui permet de caractériser le signal qu’on doit obtenir. Un tel model s’appuie sur la définition de l’interaction entre les pixels et qui est caractérisé par deux aspects :

(i) la similarité photométrique entre les pixels

(ii) la distance spatiale entre les pixels qui peut être comparée à une grandeur d’échelle. La première partie de la thèse introduit un nouveau modèle non paramétrique d’image. Ce modèle permet d’obtenir une description adaptative de l’image en utilisant des noyaux de taille variable obtenue `a partir d’une étape de classification effectuée au préalable. La deuxième partie introduit une autre approche pour décrire la dépendance entre pixels d’un point de vue géométrique. Ceci est effectué `a l’aide d’un modèle statistique de la co-occurrence entre les observations de point de vue géométrique. La dernière partie est une nouvelle technique de sélection automatique (pour chaque pixel) de la taille des noyaux utilisé au cours du filtrage. Cette thèse est conclue avec l’application de cette dernière approche dans différents contextes de filtrage ce qui montre sa flexibilité vis-à-vis des contraintes liées aux divers problèmes traités.

Références Bibliographiques

[1] J. G. Abbott and F. L. Thurstone. Acoustic speckle: Theory and experimental analysis. Ultrason. Imag, 1:303-324, 1979.

[2] A. Achim, A. Bezerianos, and P. Tsakalides. Novel bayesian multiscale method for speckle removal in medical ultrasound images. IEEE trans. on Medical Imaging, 20:772-783, August 2001.

[3] M. Aharon, M. Elad, and A. Bruckstein. K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation. IEEE trans. on Signal Processing, 54(11):4311-4322, 2006.

[4] L. Alvarez, F. Guichard, P.L. Lions, and J.M. Morel. Axioms and fundamental equations in image processing. Archive for Rational Mechanics and Analysis, 123:199-257, 1993.

[5] L. Alvarez, P.L. Lions, and J.M. Morel. Image selective smoothing and edge detection by nonlinear diffusion, ii. Journal of Numerical Analysis, 29(3):845-866, 1992.

[6] M. Arulampalam, S. Maskell, N. Gordon, and T. Clapp. A tutorial on particle filters for online non-linear/non-gaussian bayesian tracking. IEEE trans. on Signal Processing, 50:174-188, 2002.

[7] G. Aubert and J.F. Aujol. A nonconvex model to remove multiplicative noise. In Int. Conf. on Scale Space Methods and Variational Methods in Computer Vision, pages 68-79, 2007.

[8] JF. Aujol and Chambolle A. Dual norms and image decomposition models. Technical Report 5130, INRIA, 2004.

[9] JF. Aujol and Chambolle A. Dual norms and image decomposition models. Int. Journal of Computer Vision, 63(1):85-104, 2005.

[10] S. Awate and R. Whitaker. Higher-order image statistics for unsupervised, information-theoretic, adaptive, image filtering. In Proc. of the IEEE Int. Conf. on Computer Vision and Pattern Recognition, pages 44-51, 2005.

[11] N. Azzabou and Paragios. Spatio-temporal speckle reduction in ultrasound sequences. In Int. Conf. on Medical Image Computing and Computer-Assisted Intervention, 2008.

[12] N. Azzabou, N. Paragios, and F. Guichard. Random walks, constrained multiple hypothesis testing and image enhancement. In Proc. of the Europ. Conf. on Computer Vision, pages 379-390, 2006.

[13] N. Azzabou, N. Paragios, and F. Guichard. Image denoising based on adapted dictionary computation. In Proc. of the IEEE Int. Conf. on Image Processing, pages 109-112, 2007.

[14] N. Azzabou, N. Paragios, and F. Guichard. Uniform and textured regions separation in natural images towards mpm adaptive denoising. In Int. Conf. on Scale Space Methods and Variational Methods in Computer Vision, pages 418-429, 2007.

[15] N. Azzabou, N. Paragios, F. Guichard, and F. Cao. Variable bandwidth image denoising using image-based noise models. In Proc. of the IEEE Int. Conf. on Computer Vision and Pattern Recognition, pages 1-7, 2007.

[16] R. Bajcsy. Computer description of textured surfaces. In International Joint Conference on Artificial Intelligence, pages 572-579, 1973.

[17] S. Basu, P. Fletcher, and R. Whitaker. Rician noise removal in diffusion tensor mri. In Int. Conf. on Medical Image Computing and Computer-Assisted Intervention, pages 117-125, 2006.

[18] E. Bennett, M. Uyttendaele, C.L. Zitnick2, R. Szeliski, and S.B. Kang. Video and image bayesian demosaicing with a two color image prior. In Proc. of the Europ. Conf. on Computer Vision, pages 508-521, 2006.

[19] F. Bergeaud and S. Mallat. Matching pursuit of images. In Proc. of the IEEE Int. Conf. on Image Processing, pages 53-56, 1995.

[20] N. Bergman. Recursive Bayesian estimation: Navigation and tracking applications. PhD thesis, Linköping Univ., Linköping, Sweden, 1999.

[21] D. P. Bertsekas. Nonlinear Programming. Athena Scientific, Belmont, MA, 1999.

[22] M. Black, G. Sapiro, D. Marimont, and D. Heeger. Robust anisotropic diffusion. IEEE trans. on Image Processing, 7:421-432, 1998.

[23] A.C. Bovik, M. Clark, and W.S. Geisler. Multichannel texture analysis using localized spatial filters. IEEE trans. on Pattern Analysis and Machine Intelligence, 12:55-73, 1990.

[24] A.M. Bruckstein and M. Elad. On sparse signal representations. In Proc. of the IEEE Int. Conf. on Image Processing, pages 3-6, 2001.

[25] A. Buades. Image and Film denoising by non-local means. PhD thesis, Universitat de les Illes Balears, 2006.

[26] A. Buades, B. Coll, and J-M. Morel. A non-local algorithm for image denoising. In Proc. of the IEEE Int. Conf. on Computer Vision and Pattern Recognition, pages 60-65, 2005.

[27] A. Buades, B. Coll, and J.M Morel. Denoising image sequences does not require motion estimation. Technical Report 2005-18, CMLA Preprint, 2005.

[28] A. Buades, B. Coll, and J.M. Morel. Image enhancement by non-local reverse heat equation. Technical Report 2006-22, CMLA Preprint, 2006.

[29] A. Buades, B. Coll, J.M Morel, and C. Sbert. Non local demosaicing. Technical Report 2007-15, CMLA Preprint, 2007.

[30] A. Buades, JM. Morel, B. Coll, F. Cao, F. Guichard, and N. Azzabou. Conservation de la taille du grain en photographie numérique. French patent N: 07 05754, Aout 2007.

[31] V. Caselles, J.M. Morel, G. Sapiro, and A. Tannenbaum. Introduction to the special issue on partial-differential equations and geometry-driven diffusion in image-processing and analysis. IEEE trans. on Image Processing, 7(3):269-273, 1998.

[32] C. A. Castano-Moraga, C. Lenglet, R. Deriche, and J. Ruiz-Alzola. A Riemannian approach to anisotropic filtering of tensor fields. Signal Processing, Special Issue on Tensor Signal Processing,, 87(2):263-276, 2007.

[33] A. Chambolle and P.L. Lions. Image recovery via total variation minimization and related problems. Numerische Mathematik, 76:167-188, 1997.

[34] C. Chefd’hotel, D. Tschumperle, R. Deriche, and O.D. Faugeras. Regularizing flows for constrained matrix-valued images. Journal of Mathematical Imaging and Vision, 20(1-2):147-162, 2004.

[35] P.C. Chen and T. Pavlidis. Segmentation by texture using correlation. IEEE trans. on Pattern Analysis and Machine Intelligence, 5(1):64-69, 1983.

[36] Y. Cheng. Mean shift, mode seeking, and clustering. IEEE trans. on Pattern Analysis and Machine Intelligence, 17:790-799, 1995.

[37] R. Coifman, Y. Meyer, and V. Wickerhauser. Wavelet analysis and signal processing. Wavelets and their applications, pages 153-173, 1992.

[38] D. Comaniciu and P. Meer. Mean shift: A robust approach toward feature space analysis. IEEE trans. on Pattern Analysis and Machine Intelligence, 15(5):603-619, 2002.

[39] D. Comaniciu, V. Ramesh, and P Meer. The variable bandwidth mean shift and data-driven scale selection. In Proc. of the IEEE Int. Conf. on Computer Vision and Pattern Recognition, volume 1, pages 438-445, 2001.

[40] O. Coulon, D. C. Alexander, and S. Arridge. Diffusion tensor magnetic resonance image regularization. Medical Image Analysis, 8(1):47-67, 2004.

[41] I. Daubechies. The wavelet transform, time-frequency localization and signal analysis. IEEE trans. on Information Theory, 36:961-1005, 1990.

[42] A. Dempster, M. Laird, and D. Rubin. Maximum likelihood from incomplete data via the em algorithm. Journal of the Royal Statistical Society, 39:1-38, 1977.

[43] R. Deriche, D. Tschumperle, C. Lenglet, and M. Rousson. Variational approaches to the estimation, regularization and segmentation of diffusion tensor images. In Faugeras Paragios, Chen, editor, Mathematical Models in Computer Vision: The Handbook. Springer, 2005 edition, 2005.

[44] K. I. Diamantaras and S. Y. Kung. Principal component neural networks: theory and applications. John Wiley & Sons, Inc., 1996.

[45] D. L. Donoho and I. M. Johnstone. Ideal spatial adaptation by wavelet shrinkage. Biometrika, 81(3):425-455, 1994.

[46] A. Doucet. On sequential simulation-based methods for bayesian filtering. Technical Report CUED/F-INFENG/TR. 310, Cambridge University Department of Engineering, 1998.

[47] A. Doucet, J. de Freitas, and N. Gordon. Sequential Monte Carlo Methods in Practice. Springer-Verlag, New York, 2001.

[48] D.Tschumperle and R.Deriche. Vector-valued image regularization with pdes: A common framework for different applications. IEEE trans. on Pattern Analysis and Machine Intelligence, 27(4):506-517, 2005.

[49] R.O. Duda and P. Hart. Pattern Classification And Scene Analysis. WileyInterscience Publication, 1973.

[50] D. Dunn and W.E. Higgins. Optimal gabor filters for texture segmentation. IEEE trans. on Image Processing, 4:947-964, 1995.

[51] A. Efros and T. Leung. Texture synthesis by non-parametric sampling. In Proc. of the Int. Conf. on Computer Vision, pages 1033-1038, 1999.

[52] K. Egiazarian, V. Katkovnik, and J. Astola. Adaptive window size image denoising based on ici rule. In Proc. of the IEEE Int. Conf. on Acoustic, Speech and Signal Processing, pages 1869-1872, 2001.

[53] M. Elad and M. Aharon. Image denoising via learned dictionaries and sparse representation. In Proc. of the IEEE Int. Conf. on Computer Vision and Pattern Recognition, pages 895-900, 2006.

[54] I. Elfadel and R. Picard. Gibbs random fields, cooccurrences, and texture modeling. IEEE trans. on Pattern Analysis and Machine Intelligence, 16(1):24-37, 1994.

[55] P. Fillard, V. Arsigny, X. Pennec, and N. Ayache. Clinical DT-MRI estimation, smoothing and fiber tracking with log-Euclidean metrics. In IEEE Int. Symp. on Biomedical Imaging: From Nano to Macro, pages 786-789, 2006.

[56] A. Foi, S. Alenius, V. Katkovnik, and K. Egiazarian. Image denoising using scale mixtures of gaussians in the wavelet domain. IEEE Sensors Journal, 7(10):1456-1461, 2007.

[57] D. Gabor. Theory of communication. J. IEE (London), 93:429-457, 1946.

[58] S. Geman and D. Geman. Stochastic relaxation, gibbs distributions, and the bayesian restoration of images. IEEE trans. on Pattern Analysis and Machine Intelligence, 6:721-741, 1984.

[59] G. Gilboa, J. Darbon, S. Osher, and T. Chan. Nonlocal convex functionals for image regularization. Technical Report 06-57, UCLA CAM Report, 2006.

[60] G. Gilboa and S. Osher. Nonlocal linear image regularization and supervised segmentation. Technical Report 06-47, UCLA CAM Report, 2006.

[61] G. Gilboa and S. Osher. Nonlocal linear image regularization and supervised segmentation. SIAM Multiscale Modeling and Simulation, 6:595-630, 2007.

[62] G. Gilboa, N. Sochen, and Zeevi Y.Y. Variational denoising of partly-textured images by spatially varying constraints. IEEE trans. on Image Processing, 24(8):2281-2289, 2006.

[63] J.W. Goodman. Some fundamental properties of speckle. J. Opt. Soc, 66:1145-1150, 1976.

[64] N. Gordon, D. Salmond, and A. Smith. Novel approach to nonlinear/non-gaussian bayesian state estimation. IEEE Proceedings on Radar and Signal Processing, 140:107-113, 1993.

[65] R.M. Haralick, K. Shanmugam, and I. Dinstein. Textural features for image classification. IEEE Transactions on Systems, Man and Cybernatics, 6:610-621, 1973.

[66] C. Herley and M. Vetterli. Wavelets and recursive filter banks. IEEE trans. on Signal Processing, 41:2536-2556, 1993.

[67] J.-B. Hiriart-Urruty and C. Lemaréchal. Fundamentals of Convex Analysis. Springer Verlag, Heidelberg, 2001.

[68] J. Huang and D. Mumford. Statistics of natural images and models. In Proc. of the IEEE Int. Conf. on Computer Vision and Pattern Recognition, pages 541-547, 1999.

[69] D. H. Hubel and T. N. Wiesel. Receptive fields, binocular interaction and functional architecture in the cat’s visual cortex. The Journal of Physiology, 160:106-154, 1962.

[70] J. Hwang, S. Lay, and A. Lippman. Nonparametric multivariate density estimation: a comparative study. IEEE trans. on Signal Processing, 42:2795-2810, 1994.

[71] Besag. J. Spatial interaction and the statistical analysis of lattice systems. Journal of the Royal Statistical Society. Series B, 36(2):192-236, 1974.

[72] A.K. Jain. Fundamentals of digital image processing. Prentice-Hall, Inc., 1989.

[73] T. Joachims. Making large-scale support vector machine learning practical. In A. Smola B. Schölkopf, C. Burges, editor, Advances in Kernel Methods: Support Vector Machines. MIT Press, Cambridge, MA, 1998.

[74] A. Katsaggelos and M. Kang. Simultaneous iterative image restoration and evaluation of the regularization parameter. IEEE trans. on Signal Processing, 40:2329-2334, 1992.

[75] C. Kervrann and J. Boulanger. Local adaptivity to variable smoothness for exemplar-based image denoising and representation. Technical Report 5624, INRIA, July 2005.

[76] Ch. Kervrann and J. Boulanger. Unsupervised patch-based image regularization and representation. In Proc. of the Europ. Conf. on Computer Vision, pages 555-567, 2006.

[77] Ch. Kervrann, J. Boulanger, and P. Coupé. Bayesian non-local means filter, image redundancy and adaptive dictionaries for noise removal. In Int. Conf. on Scale Space Methods and Variational Methods in Computer Vision, pages 520-532, 2007.

[78] B.B. Kimia, A. Tannenbaum, and S.W. Zucker. On the evolution of curves via a function of curvature. i. the classical case. Journal Mathematical Analysis Applications, 163:438-458, 1992.

[79] R. Kimmel. Demosaicing: Image reconstruction from color CCD samples. IEEE trans. on Image Processing, 8(9):1221-1228, 1999.

[80] R. Kimmel, R. Malladi, and N. Sochen. Image processing via the beltrami operator. In Proc. of the Asian. Conf. on Computer Vision, pages 574-581, 1998.

[81] R. Kimmel, N.A. Sochen, and R. Malladi. From high energy physics to low level vision. In Proc. of the Int. Conf. on Scale-Space Theory in Computer Vision, pages 236-247, 1997.

[82] R. Kimmel, N.A. Sochen, and R. Malladi. Images as embedding maps and minimal surfaces: A unified approach for image diffusion. In Proc. of the IEEE Int. Conf. on Image Processing, pages 368-371, 1997.

[83] S. Kindermann, S. Osher, and P. Jones. Deblurring and denoising of images by nonlocal functionals. SIAM Multiscale Modeling and Simulation, 4:1091-1115, 2005.

[84] G. Kitagawa. Monte carlo filter and smoother for non-gaussian nonlinear state space models. Journal of Computational and Graphical Statistics, 5:1-25, 1996.

[85] J.J. Koenderink. The structure of images. BioCyber, 50, 1984.

[86] P. Kornprobst and G. Aubert. Mathematical Problems in Image Processing Partial Differential Equations and the Calculus of Variations. Springer, 2002.

[87] P. Kornprobst, R. Deriche, and A. Gilles. Nonlinear operators in image restoration. In Proc. of the IEEE Int. Conf. on Computer Vision and Pattern Recognition, pages 325-330, 1997.

[88] H. Krim, D. Tucker, S. Mallat, and D. Donoho. On denoising and best signal representation. IEEE trans. on Information Theory, 45(7):2225-2238, 1999.

[89] D. Le Bihan, J.-F. Mangin, C. Poupon, C. A. Clark, S. Pappata, N. Molko, and H. Chabriat. Diffusion tensor imaging: concepts and applications. Journal of Magnetic Resonance Imaging, 13:534-546, 2001.

[90] E. Le Pennec and S. Mallat. Sparse geometric image representations with bandelets. IEEE trans. on Image Processing, pages 423-438, 2005.

[91] A. Lee, K. Pedersen, and D. Mumford. The nonlinear statistics of high-contrast patches in natural images. Int. Journal of Computer Vision, pages 83-103, 2003.

[92] S. Lee. Digital image smoothing and the sigma filter. CVGIP, 24(2):255-269, November 1983.

[93] O. V. Lepski, E. Mammen, and V. G. Spokoiny. Optimal spatial adaptation to inhomogeneous smoothness: an approach based on kernel estimates with variable bandwidth selectors. Annals of Statistics, 25(3):929-947, 1997.

[94] M. S. Lewicki and T. J. Sejnowski. Learning overcomplete representations. Neural Computation, 12(2):337-365, 2000.

[95] S. Z. Li. Markov Random Field Modeling in Computer Vision. Springer, 1995.

[96] C. Liu, W.T. Freeman, R. Szeliski, and S.B. Kang. Noise estimation from a single image. In Proc. of the IEEE Int. Conf. on Computer Vision and Pattern Recognition, pages 901-908, 2006.

[97] M.R. Luettgen, W.C. Karl, A.S. Willsky, and R. Tenney. Multiscale representations of markov random fields. IEEE trans. on Signal Processing, 41(12):3377-3396, 1993.

[98] M. Mahmoudi and G. Sapiro. Fast image and video denoising via nonlocal means of similar neighborhoods. IEEE, Signal Processing Letters, 12:839-842, 2005.

[99] J. Mairal, M. Elad, and G. Sapiro. Sparse representation for color image restoration. IEEE trans. on Image Processing, 17(1):53-69, 2008.

[100] J. Mairal, G. Sapiro, and M. Elad. Multiscale sparse image representation with learned dictionaries. In Proc. of the IEEE Int. Conf. on Image Processing, pages 105-108, 2007.

[101] R. Malladi and J.A. Sethian. Flows under min/max curvature flow and mean curvature: Applications in image processing. In Proc. of the Europ. Conf. on Computer Vision, pages 251-262, 1996.

[102] S. Mallat. A theory for multiresolution signal decomposition: the waveletrepresentation. IEEE trans. on Pattern Analysis and Machine Intelligence, 11:674-693, 1989.

[103] S. Mallat. A Wavelet Tour of Signal Processing. Academic Press, 1998.

[104] Lee Markosien. A motion-compensated filter for ultrasound image sequences. Technical report, Providence, RI, USA, 1996.

[105] M. Martín-Fernández, C.F. Westin, and C. Alberola-López. 3D Bayesian regularization of diffusion tensor MRI using multivariate Gaussian Markov random fields. In Int. Conf. on Medical Image Computing and Computer-Assisted Intervention, pages 351-359, 2004.

[106] G. McLachlan, D. Peel, and P. Prado. Maximum likelihood clustering via normal mixture models. Signal Processing Image Communication, 8:105-111, 1996.

[107] Y. Meyer. Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures. American Mathematical Society, 2001.

[108] L. Moisan. Affine plane curve evolution: A fully consistent scheme. IEEE trans. on Image Processing, 7(3):411-420, 1998.

[109] N. Neji, R. Azzabou, G. Fleury, and N. Paragios. Diffusion tensor estimation, regularization and classification. In N. Ayache N.Paragios, J. Duncan, editor, Biomedical Image Analysis: Methodologies and Applications. Springer, 2008 edition, 2008.

[110] R. Neji, N. Azzabou, N. Paragios, and G. Fleury. A convex semi-definite positive framework for dti estimation and regularization. In Int. Symp. in Visual Computing,, pages 220-229, 2007.

[111] A. Ogier, P. Hellier, and C. Barillot. Speckle reduction on ultrasound image by variational methods and adaptive Lagrangian multipliers. In IEEE Int. Symp. on Biomedical Imaging: From Nano to Macro, pages 547-550, 2004.

[112] S. Paris and F. Durand. A fast approximation of the bilateral filter using a signal processing approach. In Proc. of the Europ. Conf. on Computer Vision, pages 568-580, 2006.

[113] E. Parzen. On the estimation of a probability density function and mode. Annals of Mathematical Statistics, 33:1065-1076, 1962.

[114] A. Perez. Markov random fields and images. Technical Report N1196, IRISA, 1998.

[115] P. Perona and J. Malik. Scale space and edge detection using anisotropic diffusion. IEEE trans. on Pattern Analysis and Machine Intelligence, 12:629-639, 1990.

[116] A. Pizurica, W. Philips, I. Lemahieu, and M. Acheroy. A versatile wavelet domain noise filtration technique for medical imaging. IEEE trans. on Medical Imaging, 22(3):323-331, 2003.

[117] J. Polzehl and V. Spokoiny. Adaptive weights smoothing with applications to image restoration. Journal of the Royal Statistical Society. Series B (Statistical Methodology), 62:335-354, 2000.

[118] K. Popat and R. W. Picard. Cluster based probability model and its application to image and texture processing. IEEE trans. on Image Processing, 6(2):268-284, 1997.

[119] J. Portilla, V. Strela, M.J. Wainwright, and E.P. Simoncelli. Image denoising using scale mixtures of gaussians in the wavelet domain. IEEE trans. on Image Processing, 12(11):1338-1351, 2003.

[120] S. Roth and M.J. Black. Fields of experts: A framework for learning image priors. In Proc. of the IEEE Int. Conf. on Computer Vision and Pattern Recognition, pages 860-867, 2005.

[121] L. Rudin and S. Osher. Total variation based image restoration with free local constraints. Proc. of the IEEE Int. Conf. on Image Processing, 1:31-35, 1994.

[122] L. Rudin, S. Osher, and E. Fatemi. Nonlinear total variation based noise removal. Physica D, 60:259-268, 1992.

[123] P. Sallee and B.A. Olshausen. Image denoising using learned overcomplete representations. In Proc. of the IEEE Int. Conf. on Image Processing, pages 381-384, 2003.

[124] R. Salvador, A. Pe ˜ na, D. Menon, T. Carpenter, J. Pickard, and Ed. Bullmore. Formal characterization and extension of the linearized diffusion tensor model. Human Brain Mapping, 24(2):144-155, 2005.

[125] S.J Sheather and M. C. Jones. A reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society. Series B (Methodological), 53:683-690, 1991.

[126] E. Simoncelli. Modeling the joint statistics of images in the wavelet domain. In Proc SPIE, 44th Annual Meeting, volume 3813, pages 188-195, 1999.

[127] S.M. Smith and J. M. Brady. SUSAN: A new approach to low level image processing. Int. Journal of Computer Vision, 23(1):45-78, 1997.

[128] B. Smolka and K. Wojciechowski. Random walk approach to image enhancement. Signal Processing, 81:465-482, 2001.

[129] N.A. Sochen, R. Kimmel, and R. Malladi. A general framework for low-level vision. IEEE trans. on Image Processing, 7(3):310-318, 1998.

[130] J.L. Starck, E.J. Candes, and D.L. Donoho. The curvelet transform for image denoising. IEEE trans. on Image Processing, 11(6):670-684, 2002.

[131] E.O. Stejskal and J.E. Tanner. Spin diffusion measurements: spin echoes in the presence of a time-dependent field gradient. Journal of Chemical Physics, 42:288-292, 1965.

[132] A.D. Szlam. Non-stationary analysis of datasets and applications. PhD thesis, Yale, 2006.

[133] A.N. Tikhonov. The regularization of ill-posed problems. Soviet. Math. Dokl. Akad. Nauk., 153(1):49-52, 1963.

[134] C. Tomasi and R. Manduchi. Bilateral filtering for gray and color images. In Proc. of the Int. Conf. on Computer Vision, pages 839-846, 1998.

[135] D. Tschumperlé. PDE’s Based Regularization of Multivalued Images and Applications. PhD thesis, Unversite de Nice Sophia Antipolis, 2002.

[136] D. Tschumperle and R. Deriche. Diffusion tensor regularization with constraints preservation. In Proc. of the IEEE Int. Conf. on Computer Vision and Pattern Recognition, pages 948-953, 2001.

[137] D. Tschumperle and R. Deriche. Vector-valued image regularization with pdes: A common framework for different applications. In Proc. of the IEEE Int. Conf. on Computer Vision and Pattern Recognition, pages 651-656, 2003.

[138] M. Tur, K.-C. Chin, and J.W. Goodman. When is speckle noise multiplicative? Applied Optics, 21:1157-1159, 1982.

[139] M. Unser. Local linear transforms for texture measurements. Signal Processing., 11:61-79, 1986.

[140] L. Vese and S. Osher. Modeling textures with total variation minimization and oscillating patterns in image processing. Journal of Scientific Computing, 19:553-572, 2003.

[141] M.J. Wainwright, E.P. Simoncelli, and A.S. Willsky. Random cascades of gaussian scale mixtures and their use in modeling natural images with application to denoising. In Proc. of the IEEE Int. Conf. on Image Processing, pages 260-263, 2000.

[142] M. Wand and M. Jones. Kernel Smoothing. Chapman & Hall,, 1995.

[143] Ching-Chun Wang. A Study of CMOS Technologies for Image Sensor application. PhD thesis, MIT, 2001.

[144] Z. Wang, B. Vemuri, Y. Chen, and T. Mareci. A constrained variational principle for direct estimation and smoothing of the diffusion tensor field from complex DWI. IEEE trans. on Medical Imaging, 23(8):930-939, 2004.

[145] J. Weickert. A review of nonlinear diffusion filtering. In Scale-Space Theory in Computer Vision, pages 3-28, 1997.

[146] J. Weickert. Coherence-enhancing diffusion filtering. Int. Journal of Computer Vision, 31:111-127, 1999.

[147] J. Weickert, C. Feddern, M. Welk, B. Burgeth, and T. Brox. PDEs for tensor image processing. In J. Weickert and H. Hagen, editors, Visualization and Processing of Tensor Fields, pages 399-414. Springer, 2006.

[148] J. Weickert, B.M. ter Haar Romeny, and M. Viergever. Image recovery via total variation minimization and related problems. Numerische Mathematik, 76(2):167-188, 1997.

[149] J. Weickert, B.M. ter Haar Romeny, and M. Viergever. Efficient and reliable schemes for nonlinear diffusion filtering. IEEE trans. on Image Processing, 7(2):398, 1998.

[150] A.S. Willsky. Multiresolution markov models for signal and image processing. Proceedings of the IEEE, 90(8):1396-1458, 2002.

[151] A.P. Witkin. Scale-space filtering. In International Joint Conf. on Artificial Intelligence, pages 1019-1022, 1983.

[152] L. P. Yaroslavsky. Local adaptive image restoration and enhancement with the use of dft and dct in a running window. Proceedings of SPIE Wavelet Applications in Signal and Image Processing, 2825:2-13, 1996.

[153] L.P. Yaroslavsky. Digital Picture Processing. Springer-Verlag New York, Inc., Secaucus, NJ, USA, 1985.

[154] Y. Yu and S.T. Acton. Speckle reducing anisotropic diffusion. IEEE trans. on Image Processing, 11(11):1260-1270, 2002.

[155] C. Yung-Gang, G. Yoshikazu, and G. Shun’ichi. Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations. J. Differ Geom, 33:-, 1991.

[156] S.C. Zhu, Y. Wu, and M. Mumford. Frame: Filters, random fields, and minimax entropy-towards a unified theory for texture modeling. In Proc. of the IEEE Int. Conf. on Computer Vision and Pattern Recognition, page 686, 1996.

[157] S.C. Zhu, Y.N. Wu, and D. Mumford. Filters, random-fields and maximum-entropy (frame): Towards a unified theory for texture modeling. Int. Journal of Computer Vision, 27(2):107-126, 1998.

Table des Matières

1. Introduction en Français - 21

1.1 Présentation du problème et Motivations - 21

1.2 Les Contributions - 22

1.3 Plan de la thèse - 24

2. Introduction - 27

2.1 Problem Statement and motivation - 27

2.2 State of the Art - 29

2.2.1 Averaging Based Filters - 30

2.2.2 PDE’s and Energy Based Image Restoration - 33

2.2.3 Image Transform and Compact Representation - 38

2.2.4 Statistical Models and Image Denoising - 42

2.3 Main Contributions - 46

2.4 Thesis Outline - 48

3. MP MAdaptive Denoising - 51

3.1 Introduction - 51

3.2 Unsupervised Information-Theoretic Adaptive Filter - 53

3.3 Unsupervised Classification of Image Pixels - 55

3.3.1 Texture Feature Extraction - 55

3.3.2 Dimensionality Reduction - 57

3.3.3 Application to Pixels Classification - 59

3.4 Non Parametric Model and Adaptive Denoising - 62

3.4.1 Bayesian Formulation of the Problem - 62

3.4.2 Non Parametric Density Estimation - 67

3.4.3 Variable Bandwidth Selection - 69

3.4.4 Marginal Posterior Maximizing - 70

3.5 Experimental Results - 72

3.6 Conclusion - 79

4. Image Reconstruction Using Particle Filters - 81

4.1 Introduction - 81

4.2 Statistical Description of Image Structure - 83

4.3 Overview of Particle Filtering Technique - 86

4.3.1 Preliminaries - 87

4.3.2 Sampling Importance Resampling Filter (SIR) - 88

4.4 Application to image restoration - 90

4.4.1 Transition Model - 91

4.4.2 Likelihood Measure - 92

4.4.3 Intensity Reconstruction - 93

4.4.4 Extension to Multiplicative Noise Model - 95

4.5 Experimental Results - 96

4.5.1 Additive Noise - 97

4.5.2 Multiplicative Noise - 98

4.6 Conclusion - 104

5. TV Based Variable Bandwidth Image Denoising - 109

5.1 Introduction - 109

5.2 Related Work - Extensions of the TV Model - 110

5.2.1 Texture Preserving Denoising Using Spatially Varying Constraints - 111

5.2.2 Image Decomposition Models - 112

5.2.3 Non Local Functional Based Regularization - 114

5.3 Variable Bandwidth Denoising Using Semi Local Quadratic Functional - 115

5.3.1 Analysis of the Denoising Model - 115

5.3.2 Bandwidth Computation - 119

5.4 On the similarity measure between patches - 121

5.4.1 New Statistical Similarity Measure Between Patches - 122

5.4.2 PCA Based Dictionary - 123

5.5 Experimental Results - 128

5.5.1 On the weight selection - 129

5.6 Conclusion - 135

6. Applications - 143

6.1 Color Image Denoising - 143

6.1.1 Noise Properties from Raw to RGB Images - 144

6.1.2 Noise Model Estimation - 146

6.1.3 The Denoising Algorithm - 147

6.1.4 Experimental Results - 149

6.1.5 Discussion - 150

6.2 Application to DTI estimation and regularization - 150

6.2.1 Introduction - 150

6.2.2 DTI Estimation and Regularization - 156

Measuring Similarities from diffusion weighted images - 157

Semi-Dfinite Positive Gradient Descent - 158

6.2.3 Experimental Validation - 160

Artificially Corrupted Tensors - 160

DTI towards Understanding the Human Skeletal Muscle - 161

6.2.4 Discussion - 164

6.3 Speckle suppression in ultrasound sequences - 165

6.3.1 Introduction - 165

6.3.2 Problem Statement - 166

6.3.3 Weights Computation - 168

6.3.4 Experimental Results - 170

6.3.5 Discussion - 172

6.4 Conclusion - 174

7. Conclusion - 175

8. Conclusion en Français - 181

8.1 Perspectives - 183

Bibliography - 187

Statistiques de consultation

Administrateurs de l'archive uniquement : éditer cet enregistrement