Jianfeng Lu, Courant Institue

Abstract:

The Empirical Mode Decomposition algorithm is a technique that aims to decompose into their building blocks functions that are the superposition of a (reasonably) small number of components, well separated in the time-frequency plane, each of which can be viewed as approximately harmonic locally, with slowly varying amplitudes and frequencies. The EMD has already shown its usefulness in a wide range of applications including meteorology, structural stability analysis, medical studies. On the other hand, the EMD algorithm contains heuristic and ad-hoc elements that make it hard to analyze mathematically.

We will discuss a method that captures the flavor and philosophy of the EMD approach, albeit using a different approach in constructing the components. A precise mathematical definition is given for a class of functions that can be viewed as a superposition of a reasonably small number of approximately harmonic components, and we prove that our method does indeed succeed in decomposing arbitrary functions in this class. Several examples, for simulated as well as real data, will be given.

This is a joint work with Ingrid Daubechies (Princeton) and Hau-Tieng

Wu (Princeton).