## Abstract

A generalization of the linear fractional integral equation u(t)= ^{u0}∂^{-α}Au(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 PeronaMalik and alike approaches. Several experiments showing the improvements achieved by our approach are provided.

Original language | British English |
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Pages (from-to) | 553-563 |

Number of pages | 11 |

Journal | Signal Processing |

Volume | 92 |

Issue number | 2 |

DOIs | |

State | Published - Feb 2012 |

## Keywords

- Convolution quadrature methods
- Fractional integrals and derivatives
- Image processing
- Volterra equations