Image structure preserving denoising using generalized fractional time integrals

Abstract

A generalization of the linear fractional integral equation u(t) = u 0 + ∂ −α 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 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.

Forward-backward processing technique for image denoising using FDZP 2D filter

“…Such limitation is removed using the non-linear models that have better edge preserving capability than linear models. The fractional calculus has been applied by numerous researchers in various fields (Kilbas, Srivastava, & Trujillo, 2006;Podlubny, 1998) related to image texture enhancement (Gao, Zhou, Zheng, & Lang, 2011;Hu, Pu, & Zhou 2011b) and Jalab and Ibrahim (2012) and image denoising (Cuesta, Kirane, & Malik, 2012;Das, 2011;Hu, Pu, & Zhou, 2011a;Miller & Ross, 1993). The results, which were computed using these operators, showed high robustness against different types of noise (Artal- Bartolo, 1994;Das, 2011) implemented a fractional integral filter using fractional integral mask windows on eight directions based on Riemann-Liouville definition of fractional calculus.…”

Adaptive active contour model driven by fractional order fitting energy

“…Up to now, fractional order differentiations/equations have been widely applied in many areas, especially in the filed of image processing [21][22][23]. Mathieu et al proposed an edge detector based on fractional differentiation [24].…”

Image Structure-Preserving Denoising Based on Difference Curvature Driven Fractional Nonlinear Diffusion

“…A class of fully fractional anisotropic diffusion models was presented by Janev et al [37] for noise removal, where spatial as well as time fractional-order derivatives are employed. Cuesta et al [38] deduced a Volterra matrix-valued equation for image noise removal from a generalization of the linear fractional integral equation. However, they still have many great potential drawbacks.…”