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.