Variable Sampling of the Empirical Mode Decomposition of Two-Dimensional Signals

Previous work on Empirical Mode Decomposition in two dimensions typically generates a residue with many extrema points. In this paper we propose an improved method to decompose an image into a number of Intrinsic Mode Functions and a residue image with a minimum number of extrema points. We further propose a method for the variable sampling of the two-dimensional Empirical Mode Decomposition. Since traditional frequency concept is not applicable in this work we introduce the concept of empiquency, short for Empirical Mode Frequency, to describe the signal oscillations. The very special properties of the Intrinsic Mode Functions are used for variable sampling in order to reduce the number of parameters to represent the image. This is done blockwise using the occurrence of extrema points of the Intrinsic Mode Function to steer the sampling rate of the block. A method of using overlapping 7x7 blocks is introduced to overcome blocking artifacts and to further reduce the number of parameters required to represent the image. The results presented here shows that an image can be successfully decomposed into a number of Intrinsic Mode Functions and a residue image with a minimum number of extrema points. The results also show that subsampling offers a way to keep the total numbers of samples generated by Empirical Mode Decomposition approximately equal to the number of pixels of the original image.