Image structure preserving denoising using generalized fractional time integrals |
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Authors: | Eduardo Cuesta Mokhtar Kirane |
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Affiliation: | a Department of Applied Mathematics, E.T.S. of Telecommunication Engineers, University of Valladolid, Spain b Laboratoire de Mathématiques, Image et Applications, Université de La Rochelle, Avenue M. Crépeau, 17042 La Rochelle Cedex, France |
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Abstract: | A generalization of the linear fractional integral equation u(t)=u0+∂−αAu(t), 1<α<2, which is written as a Volterra matrix-valued equation when applied as a pixel-by-pixel technique is proposed in this paper for image denoising (restoration, smoothing, etc.). Since the fractional integral equation interpolates a linear parabolic equation and a hyperbolic equation, the solution enjoys intermediate properties. The Volterra equation we propose is well-posed for all t>0, and allows us to handle the diffusion by means of a viscosity parameter instead of introducing nonlinearities in the equation as in the Perona-Malik and alike approaches. Several experiments showing the improvements achieved by our approach are provided. |
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Keywords: | Image processing Fractional integrals and derivatives Volterra equations Convolution quadrature methods |
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