Abstract

We introduce and study a variational model for signal and image denoising based on Riemann-Liouville fractional derivatives of every positive order higher than zero. Both the one-dimensional and two-dimensional cases are studied. The model exploits an L1L^1 fitting data term together with both right and left Riemann-Liouville fractional derivatives as regularizing terms, with the aim of achieving an orientation independent analysis. To provide evidence of effectiveness for the proposed model we introduce a discretisation based on a second-order consistent Grünwald Letnikov scheme and show some numerical simulations aiming to denoise images corrupted by impulsive noise, which can be well modeled by the Laplace distribution.

Author information

Contact details are reproduced from the original publication and may be historical.

Keywords

  • Symmetrized fractional variation
  • Riemann-Liouville fractional derivatives
  • Grünwald-Letnikov formulas
  • discretization of fractional derivatives
  • calculus of variations
  • image denoising
  • Abel equation
  • bounded variation functions

Mathematics Subject Classification

26A33, 26A45, 65K10

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Suggested citation

A. Lanza, A. Leaci, S. Morigi, F. Tomarelli. “High Order Symmetrised Fractional Variation for Signal and Image Analysis.” Journal of Convex Analysis 33 (2026), No. 3&4, 925–952. https://doi.org/10.68381/jca33051

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Published by Heldermann Verlag, 2026. Rights now held by Banach Press LLC.