Image structure preserving denoising using generalized fractional time integrals.

Edurado Cuesta (1) , Mokhtar Kirane (2) , Salman Amin Malik (2)

1 IES - Industrial Engineering School
2 MIA - Mathématiques, Image et Applications - EA 3165

A generalization of the linear fractional integral equation u(t) = u0+∂−Au(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, and allows us to handle the diffusion by means of some viscosity parameters 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.

Domaines: Traitement des images [eess.IV]

Edurado Cuesta, Mokhtar Kirane, Salman Amin Malik. Image structure preserving denoising using generalized fractional time integrals.. 2011. ⟨hal-00437341v2⟩