A PDE model for 2D intrinsic mode functions

In this paper, we provide some theoretical contributions on the study of the 2D empirical mode decomposition (EMD). For doing this, we model the 2D sifting process (SP) in a suitable way, which helps us prove its convergence. Indeed, we prove that the 2D SP converges towards the solution of a fourth order partial differential equation (PDE). We show that 2D intrinsic mode functions (IMFs) are well approximated by the so-called 2D ¿-IMFs, which are defined based on such PDE solutions. Numerical simulations for both synthetic and real images show that the proposed 2D PDE-based EMD behaves like the classical EMD. Not only has the presented work the benefit of a theoretical contribution on the 2D EMD, but also, it relieves the tedious problems of surface interpolation necessary for envelopes´ construction and improves the classical 2D EMD.