Image structure preserving denoising using generalized fractional time integrals

A generalization of the linear fractional integral equation u(t) = u(0) + partial derivative Au-alpha(t), 1 < alpha < 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. (C) 2011 Elsevier B.V. All rights reserved.