Abstract
We propose a fast algorithm for image denoising, which is based on a dual formulation of a recent denoising model involving the total variation minimization of the tangential vector field under the incompressibility condition stating that the tangential vector field should be divergence free. The model turns noisy images into smooth and visually pleasant ones and preserves the edges quite well. While the original TV-Stokes algorithm, based on the primal formulation, is extremely slow, our new dual algorithm drastically improves the computational speed and possesses the same quality of denoising. Numerical experiments are provided to demonstrate practical efficiency of our algorithm.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Phys. D 60(1-4), 259–268 (1992)
Chan, T., Marquina, A., Mulet, P.: High-order total variation-based image restoration. SIAM J. Sci. Comput. 22(2), 503–516 (2000)
Chambolle, A., Lions, P.L.: Image recovery via total variation minimization and related problems. Numer. Math. 76, 167–188 (1997)
Lysaker, O., Lundervold, A., Tai, X.C.: Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time. IEEE Trans. Imag. Proc. 12, 1579–1590 (2003)
Rahman, T., Tai, X.C., Osher, S.: A tv-stokes denoising algorithm. In: Sgallari, F., Murli, A., Paragios, N. (eds.) SSVM 2007. LNCS, vol. 4485, pp. 473–483. Springer, Heidelberg (2007)
Litvinov, W., Rahman, T., Tai, X.C.: A modified tv-stokes model for image processing (submitted) (2008)
Lysaker, O.M., Osher, S., Tai, X.C.: Noise removal using smoothed normals and surface fitting. IEEE Transaction on Image Processing 13(10), 1345–1357 (2004)
Bertalmio, M., Bertozzi, A., Sapiro, G.: Navier-stokes, fluid dynamics, and image and video inpainting. In: Proc. IEEE Computer Vision and Pattern Recognition (CVPR) (2001)
Tai, X., Osher, S., Holm, R.: Image inpainting using tv-stokes equation. Image Processing based on partial differential equations (2006)
Chambolle, A.: An algorithm for total variation minimization and applications. J. Math. Imaging Vis. 20(1-2), 89–97 (2004)
Carter, J.: Dual methods for total variation-based image restoration. PhD thesis, UCLA (2001)
Chan, T.F., Golub, G.H., Mulet, P.: A nonlinear primal-dual method for total variation-based image restoration. SIAM J. Sci. Comput. 20(6), 1964–1977 (1999)
Bresson, X., Cham, T.F.: Fast minimization of the vectorial total variation norm and applications to color image processing. CAM Report 07-25 (2007)
Ciarlet, P.G., Jean-Marie, T., Bernadette, M.: Introduction to numerical linear algebra and optimisation. Cambridge University Press, Cambridge (1989)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Elo, C.A., Malyshev, A., Rahman, T. (2009). A Dual Formulation of the TV-Stokes Algorithm for Image Denoising. In: Tai, XC., Mørken, K., Lysaker, M., Lie, KA. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2009. Lecture Notes in Computer Science, vol 5567. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02256-2_26
Download citation
DOI: https://doi.org/10.1007/978-3-642-02256-2_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02255-5
Online ISBN: 978-3-642-02256-2
eBook Packages: Computer ScienceComputer Science (R0)