On analysis of bi-dimensional component decomposition via BEMD

This paper investigates how the bi-dimensional empirical mode decomposition (BEMD) behaves in digital images via two components. First, some definitions of components are given. Then the theoretical analysis is presented to show that in digital images there might be sparse extrema sets and the sifting process of BEMD converges to the true component provided that the sparse extrema sets do exist. Also, the feature of 2D component in digital images is explored via composite two-component signals. The three-dimensional cubes disclosing the performance of BEMD are presented, which turn out to be in good agreement with intuition and physical interpretation. This paper has also shown that the sampling period, the cross-angle, the amplitude ratio and the frequency ratio between the components will affect the separation of them and some instructive conclusions are achieved as well. The theoretical analysis is provided for analyzing the observed behaviors and supported by numerical experiments. The main aim of this study is primarily to contribute to a better understanding of the possibilities and limitations offered by BEMD in digital images.