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| HAL : hal-00477356, version 2 |
| arXiv : 1004.5193 |
| DOI : 10.1016/j.cnsns.2011.07.001 |
| Fiche détaillée |  Récupérer au format |
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| Communications in Nonlinear Science and Numerical Simulation 17, 2 (2012) 867-881 |
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| Versions disponibles : | v1 (29-04-2010) | v2 (28-05-2010) |
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| Simultaneous denoising and enhancement of signals by a fractal conservation law |
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| Pascal Azerad 1Afaf Bouharguane 1 |
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| (02/2012) |
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| In this paper, a new filtering method is presented for simultaneous noise reduction and enhancement of signals using a fractal scalar conservation law which is simply the forward heat equation modified by a fractional anti-diffusive term of lower order. This kind of equation has been first introduced by physicists to describe morphodynamics of sand dunes. To evaluate the performance of this new filter, we perform a number of numerical tests on various signals. Numerical simulations are based on finite difference schemes or Fast and Fourier Transform. We used two well-known measuring metrics in signal processing for the comparison. The results indicate that the proposed method outperforms the well-known Savitzky-Golay filter in signal denoising. Interesting multi-scale properties w.r.t. signal frequencies are exhibited allowing to control both denoising and contrast enhancement. |
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| 1 : | Institut de Mathématiques et de Modélisation de Montpellier (I3M) |
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CNRS : UMR5149 – Université Montpellier II - Sciences et Techniques du Languedoc |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles Sciences de l'ingénieur/Traitement du signal et de l'image Informatique/Traitement du signal et de l'image |
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| fractal operator – fractional calculus – Fourier transform – PDEs filters – denoising – enhancement – fast Fourier transform (FFT) – finite difference scheme – Savitzky-Golay filter. |
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| hal-00477356, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00477356 | |
| oai:hal.archives-ouvertes.fr:hal-00477356 | |
| Contributeur : Pascal Azerad | |
| Soumis le : Vendredi 7 Mai 2010, 11:38:33 | |
| Dernière modification le : Mardi 6 Septembre 2011, 09:17:03 | |
