Symmetrised fractional variation with L1 fidelity for signal denoising via Grünwald-Letnikov scheme

Alessandro Lanza, Antonio Leaci, Serena Morigi and Franco Tomarelli

Applied Mathematics and Computation, 2025, vol. 500, issue C

Abstract: We define, study and implement the model SFV-L1: a variational approach to signal analysis exploiting the Riemann-Liouville (RL) fractional calculus. This model incorporates an L1 fidelity term alongside fractional derivatives of the right and left RL operators to act as regularizers. This approach aims to achieve an orientation-independent protocol. The model is studied in the continuous setting and discretized in one dimension by means of a second-order consistent scheme based on approximating the RL fractional derivatives by a truncated Grünwald-Letnikov (GL) scheme. The discrete optimization problem is solved using an iterative approach based on the alternating direction method of multipliers, with guaranteed convergence.

Keywords: Fractional variation; Total variation; Riemann-Liouville fractional derivatives; Grünwald-Letnikov scheme; Functions of bounded variation; Discretization of fractional derivatives; Calculus of variations; Abel equation; Signal analysis; Multi-parameter whiteness principle (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:500:y:2025:i:c:s0096300325001560

DOI: 10.1016/j.amc.2025.129429

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