Abstract
The aim of this paper is to construct a model which decomposes a 3D image into two components: the first one containing the geometrical structure of the image, the second one containing the noise. The proposed method is based on a second order variational model and an undecimated wavelet thresholding operator. The numerical implementation is described, and some experiments for denoising a 3D MRI image are successfully performed. Future prospects are finally exposed.
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References
Bergounioux, M.: On Poincare-Wirtinger inequalities in spaces of functions of bounded variation. [hal-00515451] version 2 (June 10, 2011)
Chambolle, A.: An algorithm for total variation minimization and applications. Journal of Mathematical Imaging and Vision 20, 89–97 (2004)
Holschneider, M., Kronland-Martinet, R., Morlet, J., Tchamitchian, P.: A real time algorithm for signal analysis with the help of the wavelet transform. In: Wavelets, Time-Frequency Methods and Phase Space, pp. 286–297. Springer, Berlin (1989)
Chambolle, A., Lions, P.L.: Image recovery via total variation minimization and related problems Numerische Mathematik. Journal of Mathematical Imaging and Vision 77, 167–188 (1997)
Chan, T., Esedoglu, S., Park, F., Yip, A.: Recent Developments in total Variation Image Restoration. CAM Report 05-01, Department of Mathematics, UCLA (2004)
Louchet, C.: Variational and Bayesian models for image denoising: from total variation towards non-local means. Universite Paris Descartes, Ecole Doctoranle Mathematiques Paris-Centre (December 10, 2008)
Ekeland, I., Remam, R.: Analyse convex et problemes variationnels. Etudes Mathematiques. Dunod (1974)
Aujol, J.-F., Chambolle, A.: Dual norms and image decomposition models. IJCV 63(1), 85–104 (2005)
Piffet, L.: Décomposition d’image par modèles variationnels - Débruitage et extraction de texture. Université d’Orléans, Pôle Universités Centre Val de Loire (Novembre 23, 2010)
Bergounioux, M., Tran, M.P.: A second order model for 3D texture extraction. In: Mathematical Image Processing. Springer Proceedings in Mathematics, vol. 5. Universite d’Orleans (2011)
Starck, J.-L., Candes, E.J., Donoho, D.L.: The Curvelet transform for Image Denoising. IEEE Transactions on Image Processing 11(6) (June 2002)
Mallat, S.: A wavelet tour of signal processing. Academic Press Inc. (1998)
Jin, Y., Angelini, E., Laine, A.: Wavelets in medical image processing: denoising, sementation and registration. Department of Biomedical Engineering, Columbia University, New York, USA
Meyer, Y.: Oscillating patterns in image processing and in some nonlinear evolution equations. The 15th Dean Jacquelines B. Lewis Memorial Lectures (March 2001)
Steidl, G., Weickert, J., Brox, T., Mrzek, P., Welk, M.: On the equivalence of soft wavelet shrinkage, total variation diffusion, total variation regularization, and sides, Tech. Rep. 26, Department of Mathematics, University of Bremen, Germany (2003)
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Tran, MP., Péteri, R., Bergounioux, M. (2012). Denoising 3D Medical Images Using a Second Order Variational Model and Wavelet Shrinkage. In: Campilho, A., Kamel, M. (eds) Image Analysis and Recognition. ICIAR 2012. Lecture Notes in Computer Science, vol 7325. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31298-4_17
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DOI: https://doi.org/10.1007/978-3-642-31298-4_17
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