The Empirical Mode Decomposition: a new formulation based on Constrained Optimization
Résumé
The empirical mode decomposition (EMD) is a relatively recent method introduced by Huang et al, whose purpose is to adaptively decompose any signal into zero-mean components, called Intrinsic Mode Functions (IMF). These IMF depend on the signal (EMD is a data-driven technique) and are in practice computed by a geometric and iterative procedure whose study is particularly complicated. From the mathematical point of view, the definition of the IMFs is somewhat unclear. Moreover, the condition of "zero local mean" suggested by Huang et al should not be fulfilled in many instances, and was leading to the introduction of weak-IMF by Sharpley and Vatchev. In this talk, we present another approach for the definition of weak-IMF based on the direct construction of the mean envelope of the signal. The definition of the mean envelope is achieved through the resolution of a quadratic programming problem with equality and inequality constraints. Some numerical experiments illustrate the validity of the approach and comparisons are carried out with the classical EMD.