Abstract
Based on some previous work on the connection between image restoration and fluid dynamics, we apply a two-step algorithm for image denoising. In the first step, using a splitting scheme to study a nonlinear Stokes equation, tangent vectors are obtained. In the second step, an image is restored to fit the constructed tangent directions. We apply a fixed point iteration to solve the total variation-based image denoising problem, and use algebraic multigrid method to solve the corresponding linear equations. Numerical results demonstrate that our algorithm is efficient and robust, and boundary conditions are satisfactory for image denoising.
Similar content being viewed by others
References
Rudin L, Osher S, Fatemi E. Nonlinear total variation based noise removal algorithm. In: Proc IEEE Int Conf Image, Austin, TX, USA, 1994. 31–25
Kinder S, Osher S, Xu J. Denoising by BV-duality. J Sci Comput, 2006, 28: 414–444
Lysaker M, Osher S, Tai X C. Noise removal using smoothed normal and surface fitting. IEEE Trans Image Proc, 2004, 13: 1345–1357
Osher S, Sole A, Vese L. Image decomposition and restoration using total variation minimization and the H1 norm. Multiscale Model Simul: A SIAM Interdis J, 2003, 1: 1579–1590
Lysaker M, Lundervold A, Tai X C. Noise removal using fourth-order partial differential equations to medical magnetic resonance images in space and time. IEEE Trans Image process, 2003, 12: 1579–1590
Tomasi C, Manduchi R. Bilateral filtering for gray and color images. In: Proceedings of the 1998 IEEE International Conference on Computer Vision, Bombay, India, 1998. 839–846
Budaes A, Coll B, Morel J M. A non-local algorithm for image denoising. In: Proc IEEE CVPR, San Diego, CA, USA, 2005. 2: 60–65
Bertalmio M, Bertozzi A L, Sapiro G. Navier-Stokes, fluid dynamics, and image and video inpainting. In: Proc Conf Comp Vision Pattern Rec, Kauai, Hawaii, USA, 2001. 355–362
Mccormick S F. Multigrid Methods, Frontiers in Applied Mathematics 3. Philadelphia: SIAM, 1987
Chang Q, Wong Y S, Fu H. On the algebraic multigrid method. J Comput Phys, 1996, 125: 279–292
Chang Q, Ma S, Lei G. Algebraic multigrid method for queueing networks. Int J Comput Math, 1999, 70: 539–552
Chang Q, Chern I. Acceleration methods for total variation-based image denoising. SIAM J Sci Comput, 2003, 25: 982–994
Frohn-Schauf C, Henn S, Witsch K. Nonlinear multigrid methods for total variation image denoising. Comput Vision Sci, 2004, 7: 199–206
Rahman T, Tai X C, Osher S. A TV-Stokes denoising algorithm. In: Lecture Notes in Computer Science. Berlin: Springer-Verlag, 2007. 473–483
Chang Q. Use of the splitting scheme and multigrid method to compute flow separation. Int J Comput Math, 1987, 7: 719–731
Vogel C R, Oman E. Iterative method for the total variation denoising. SIAM J Sci Comput, 1996, 17: 227–238
Oosterlee C W, Washio T. Krylov subspace acceleration of nonlinear multigrid with application to recirculating flows. SIAM J Sci Comput, 2000, 21: 1670–1690
Chang Q, Wang W C, Xu J. A method for total variation-based reconstruction of noisy and blurred images. In: Tai X, Lie K, Chan T, et al. eds. Image Processing Based on Partial Differential Equations. Heidelberg: Springer, 2006. 92–108
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chang, Q., Tai, X. & Xing, L. Application of splitting scheme and multigrid method for TV-Stokes denoising. Sci. China Inf. Sci. 54, 745–756 (2011). https://doi.org/10.1007/s11432-011-4204-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11432-011-4204-0