Current research

Signal and image analysis using the squared eigenfunctions of Shrodinger operator


A new signal analysis method has been proposed in [1]. The idea consists is decomposing the signal using a family of a spatially shifted and localized functions, which are given by the squared L2-normalized eigenfunctions associated to the discrete spectrum of the one dimensional semi-classical Schrodin​ger operator, with the signal considered as a potential of this operator.  This method has been denoted in [1] SCSA for Semi-Classical Signal Analysis. This method has been recently extended to two dimensions for image analysis

 Besides its interesting localization property, the SCSA method has proved its performance in some applications. For instance, interesting results have been obtained when applying the SCSA method to the analysis of arterial blood pressure signals [1,2].  Moreover, it has been shown in [3], that the SCSA method can cope with noisy signals, making this method a potential tool for denoising.

Our objectives are 

  1. Study the properties of the SCSA
  2. Extend the SCSA to two dimensions for image analysis 
  3. Study the filtering properties of the SCSA 
  4. Apply the SCSA to different applications with a focus on biomedical signals/images (Magnetic resonance spectroscopy, functional Near Infrared Spectroscopy)

[1]  T.M. Laleg-Kirati, E. Cr_epeau and M. Sorine, Semi-classical signal analysis, Mathematics of Control, Signals, and Systems (MCSS) Journal, Volume 25, Issue 1 (2013), 37-61

[2]  T.M. Laleg-Kirati, C.M_edigue, Y. Papelier, F. Cottin and A. Van de Louw, Validation of a semi-classical Signal analysis method for Stroke volume variation assessment: a comparison with the PiCCO technique, Annals of Biomedical Engineering, Volume 38, Number 12 (2010), 3618-3629.

[3] D.Y. Liu and T.M. Laleg-Kirati, Mathematical properties of a semi-classical signal analysis method: noisy signal case, 1st International Conference on Systems and Computer Science, Villeneuve dascq, France (2012).