About a Partial Differential Equation-based interpolator for signal envelope computing: Existence Results and Applications

Oumar Niang (1, 2, 3) , Abdoulaye Thioune (1) , Eric Deléchelle (1, 4) , Mary Teuw Niane (2) , Jacques Lemoine (1)

1 LISSI - Laboratoire Images, Signaux et Systèmes Intelligents
2 LANI - Laboratoire d'Analyse Numérique et Informatique [Sénégal]
3 Ecole polytechnique de Thiès
4 LERISS - Laboratoire d'étude et de recherche en instrumentation, signaux et systèmes

This paper models and solves the mathematical problem of interpolating characteristic points of signals by a Partial Differential Equation (PDE) based approach. The existence and uniqueness results are established in an appropriate space whose regularity is similar to cubic spline one. We show how this space is suitable for the Empirical Mode Decomposition (EMD) sifting process. Numerical schemes and computing applications are also presented for signal envelopes calculation. The test results show the usefullness of the new PDE-interpolator in some pathological cases like for input class functions that are not so regular as in the cubic splines case. Some image filtering tests strengthen the demonstration of PDE interpolator performance.

Mots clés: Denoising; Empirical Mode Decomposition; Partial Differential Equations; Signal and Image Restoration; Signal Representation; Upper and Lower Envelope

Domaines: Autre

Oumar Niang, Abdoulaye Thioune, Eric Deléchelle, Mary Teuw Niane, Jacques Lemoine. About a Partial Differential Equation-based interpolator for signal envelope computing: Existence Results and Applications. International Scholarly Research Notices, 2013, 2013, pp.18. ⟨10.1155/2013/605035⟩. ⟨hal-00833553⟩