Master's Defence | Heming Wang, A Novel Diffusion-based Empirical Mode Decomposition Algorithm for Signal and Image Analysis

M3-4206

Candidate

Heming Wang | Applied Math, University of Waterloo

Title

A Novel Diffusion-based Empirical Mode Decomposition Algorithm for Signal and Image Analysis

Abstract

In the area of signal analysis and processing, the Fourier transform and wavelet transform are widely applied.
Empirical Mode Decomposition(EMD) was proposed as an alternative frequency analysis tool.
Although shown to be effective when analyzing non-stationary signals,
the algorithmic nature of EMD makes the theoretical analysis and formulation difficult.
Futhermore, it has some limitations that affect its performance.

In this thesis, we introduce some methods to extend or modify EMD, in an effort to provide a rigorous mathematical basis for it,
and to overcome its shortcomings.
We propose a novel diffusion-based EMD algorithm that replaces the interpolation process by a diffusion equation, and directly construct the mean curve (surface) of a signal (image).
We show that the new method simplifies the mathematical analysis,
and provides a solid theory that interprets the EMD mechanism.
In addition, we apply the new method to the 1D and 2D signal analysis showing its possible applications in audio and image signal processing.
Finally, numerical experiments for synthetic and real signals (both 1D and 2D) are presented. 
Simulation results demonstrate that our new algorithm can overcome some of the shortcomings of EMD,
and require much less computation time.