Euler’s Approximations to Image Reconstruction
In this paper we present a new method to reconstruction of images with additive Gaussian noise. In order to solve this inverse problem we use stochastic differential equations with reflecting boundary (in short reflected SDEs). The continuous model of the image denoising is expressed in terms of such equations. The reconstruction algorithm is based on Euler’s approximations of solutions to reflected SDEs.
We consider a classical Euler scheme with random terminal time and controlled parameter of diffusion. The reconstruction time of our method is substantially reduced in comparison with classical Euler’s scheme. Our numerical experiments show that the new algorithm gives very good results and compares favourably with other image denoising filters.
KeywordsWiener Process Noisy Image Image Denoising Reconstruction Time Terminal Time
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- 1.Aubert, G., Barlaud, M., Charbonnier, P., Blanc-Féraud, L.: Two Deterministic Half-Quadratic Regularization Algorithms for Computed Imaging. In: Image Processing, Proceedings ICIP 1994, pp. 168–172 (1994)Google Scholar
- 6.El Karoui, N., Mazliak, L. (eds.): Backward stochastic differential equations. Pitman Research Notes in Mathematics Series. Longman (1997)Google Scholar
- 14.Unal, G., Ben-Arous, G., Nain, D., Shimkin, N., Tannenbaum, A., Zeitouni, O.: Algorithms for stochastic approximations of curvature flows. In: Image Processing, Proceedings ICIP 2003, vol. 2–3, pp. 651–654 (2003)Google Scholar