Image structure preserving denoising using generalized fractional time integrals

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, has been proposed for image denoising (restoration, smoothing,...). 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 non linearities in the equation as in the Perona–Malik and alike approaches. Several experiments showing the improvements achieved by our approach are provided.