Title :
A PDE model for 2D intrinsic mode functions
Author :
Diop, El Hadji S ; Alexandre, R. ; Boudraa, A.O.
Author_Institution :
Groupe ASM, Ecole Navale, Brest-Armees, France
Abstract :
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.
Keywords :
image processing; interpolation; partial differential equations; 2D empirical mode decomposition; 2D intrinsic mode functions; 2D sifting process model; IMF; PDE model; envelope estimation; fourth order partial differential equation model; image processing domains; surface interpolation; Convergence; Image converters; Image processing; Interpolation; Numerical simulation; Partial differential equations; Signal generators; Signal processing; Statistics; Time series analysis;
Conference_Titel :
Image Processing (ICIP), 2009 16th IEEE International Conference on
Conference_Location :
Cairo
Print_ISBN :
978-1-4244-5653-6
Electronic_ISBN :
1522-4880
DOI :
10.1109/ICIP.2009.5413798