SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Contributed Talk

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Stability of finite difference schemes for complex reaction-diffusion processes

A. Araújo, S. Barbeiro and P. Serranho

Abstract
Complex diffusion is a commonly used denoising procedure in image processing [3]. In particular, nonlinear complex diffusion proved to be a numerically well conditioned technique that have been successfully applied in medical imaging despeckling [2]. The stability properties of a class of finite difference schemes for the nonlinear complex diffusion equation, where both explicit and implicit schemes were considered, was studied in [1]. In the present talk we extend those results for nonlinear complex reaction-diffusion equations discretized with both implicit and semi-implicit finite differences schemes. Some numerical results for despeckling optical coherence tomograms from the human retina, obtained in the context of a collaboration with the Institute of Biomedical Research in Light and Image (IBILI), a research institution of the Faculty of Medicine of the University of Coimbra, are also presented.

Bibliography
[1] A. Araújo, S. Barbeiro and P. Serranho. Stability of finite difference schemes for complex diffusion processes, SIAM J. Numer. Anal., 50 (3) (2012) 1284-1296.
[2] R. Bernardes, C. Maduro, P. Serranho, A. Araújo, S. Barbeiro and J. Cunha-Vaz. Improved adaptive complex diffusion despeckling filter, Optics Express, 18 (23) (2010) 24048-24059.
[3] G. Gilboa, N. Sochen and Y. Zeevi. Image enhancement and denoising by complex diffusion processes, IEEE Trans Pattern Anal Mach Intell, 26 (8) (2004) 1020-1036.

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