Study of empirical mode decomposition in signal analysis

This research proposal is submitted to continue an existing scientific collaboration with Prof. Ingrid Daubechies (of Princeton University) in the domain of signal analysis. We are studying the so-called Empirical Mode Decomposition method (EMD), a relatively new technique in signal analysis. Our goal is to address some of the weaknesses of this method (lack of theoretical foundation, inefficient algorithm) by reformulating it in the context of differential equations of Sturm-Liouville type (development of an alternative EMD). Among the topics of intrests are:
- finding a variational problem that gives rise to a sparse decomposition
- development of an efficient algorithm
- studying the stability of the decomposition (for noisy signals)
- applications.