Filtering properties of the Semi-classical signal/image Analysis method.

Filtering properties of the Semi-classical signal/image Analysis method.

Internship Description

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 Schrodinger 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. In the proposed project, the student will study the filtering properties of the SCSA. He will focus on developing an optimization algorithm to compute the optimal value for a key parameter on the method. Validation tests will be done on real data, which include some medical signals/images used to extract relevant information on the patient. ​ 


Faculty Name

Field of Study

​​Computer, Electrical, & Mathematical