Abstract
In this paper a novel approach for image denoising using stochastic differential equations (SDEs) is presented. In proposed method a controlled parameter to Euler’s approximations of solutions to SDEs with reflecting boundary is added. It is shown that modified diffusion gives very good results for Gaussian noise source models and compares favourably with other image denoising filters.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Gilles Aubert and Pierre Kornprobst (2002). Mathematical problems in image processing. Volume 147 of Applied Mathematical Sciences, Springer-Verlag, New York.
Gilles Aubert and Michel Barlaud and Pierre Charbonnier and Laure Blanc-Féraud (1994). Two Deterministic Half-Quadratic Regularization Algorithms for Computed Imaging. In: Proceedings of the International Conference on Image Processing. volume II, pages 168–172.
Dariusz Borkowski (2007). Chromaticity Denoising using Solution to the Skorokchod Problem. In: Proceedings of the International Conference on PDE-Based Image Processing and Related Inverse Problems, CMA, Oslo, August 8–12, 2005. Editors: X.-C. Tai, K.-A. Lie, T.F. Chan, and S. Osher. Series: Mathematics and Visualization, Springer Verlag, p. 149–161.
Emad Fatemi and Leonid I. Rudin and Stanley Osher (1992). Nonlinear total variation based noise removal algorithms. In: Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics: computational issues in nonlinear science. Physica D: Nonlinear Phenomena, Volume 60, Issue 1–4, p. 259–268.
Jitendra Malik and Pietro Perona (1990). Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(7):629–639.
Leszek Słomiński (2001). Euler’s approximations of solutions of SDEs with reflecting boundary. Stochastic Processes and Their Applications, 94:317–337.
Hiroshi Tanaka (1979). Stochastic differential equations with reflecting boundary condition in convex regions. Hiroshima Math. J., 9(1):163–177.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Borkowski, D. (2007). Modified diffusion to Image Denoising. In: Kurzynski, M., Puchala, E., Wozniak, M., Zolnierek, A. (eds) Computer Recognition Systems 2. Advances in Soft Computing, vol 45. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75175-5_12
Download citation
DOI: https://doi.org/10.1007/978-3-540-75175-5_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-75174-8
Online ISBN: 978-3-540-75175-5
eBook Packages: EngineeringEngineering (R0)