Abstract
In this paper we present a new method of reconstruction of vector-valued images with additive Gaussian noise. In order to solve this inverse problem we use stochastic differential equations with reflecting boundary. The reconstruction algorithm is based on Euler’s approximations of solutions of such equations. We consider Euler scheme with random terminal time and controlled parameter of diffusion which is driven by geometry of \(\mathbf R^n\)- valued noisy image. Our numerical experiments show that the new approach gives very good results and compares favourably with deterministic partial differential equation methods.
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Keywords
- Stochastic Differential Equation
- Wiener Process
- Stochastic Approximation
- Noisy Image
- Anisotropic Diffusion
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Borkowski, D. (2013). Stochastic Approximation to Reconstruction of Vector-Valued Images. In: Burduk, R., Jackowski, K., Kurzynski, M., Wozniak, M., Zolnierek, A. (eds) Proceedings of the 8th International Conference on Computer Recognition Systems CORES 2013. Advances in Intelligent Systems and Computing, vol 226. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00969-8_38
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DOI: https://doi.org/10.1007/978-3-319-00969-8_38
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