Three-dimensional empirical mode decomposition (TEMD): A fast approach motivated by separable filters

Empirical mode decomposition (EMD) has emerged as a powerful tool for signal/image processing. However, extending the EMD to its three-dimensional (3D) version remains a challenging task due to the enormous computational effort. In this paper, we propose a fast 3D EMD (TEMD) to decompose a volume into several 3D intrinsic mode functions (TIMFs). Two strategies are introduced to accelerate the TEMD. On the one hand, the distances among extrema, which can be used to identify the filter sizes, are effectively calculated by 3D Delaunay triangulation (DT). On the other hand, separable filters are adopted to generate the envelopes. Rather than performing a 3D filter, we separately apply a one-dimensional (1D) filter three times to obtain the same results with much less computational requirements. Simulation results demonstrate that the proposed TEMD method significantly speeds up the calculation and yields improved decomposition performance on synthetic and real world data.