The complex bidimensional empirical mode decomposition

A new method for computing complex bidimensional empirical mode decomposition (BEMD) is presented in this paper. The proposed complex-BEMD uses four quadrant spectra to apply standard BEMD to four real-valued 2D signals. The so-generated intrinsic mode functions (IMFs) are 2D complex-valued, which facilitates the extension of the standard BEMD to the complex domain. The proposed complex-BEMD can be successful for the analysis of real-world 2D complex-valued signals, such as 2D NMR signals. Moreover, the proposed complex-BEMD can be applied for color image processing. A simple color image fusion algorithm based upon the proposed complex-BEMD has also been developed to have the exhibition of the potential. By our proposed complex-BEMD and image fusion algorithm, the well-fused results can be obtained, if the mode mixing in BEMD is alleviated.

► A formula for the perfect reconstruction of 2D Hilbert transforms is proposed.
► We develop a complex BEMD algorithm for 2D complex signals.
► We show the complex BEMD can be used for analysis of the 2D natural complex signal.
► We developed a fusion algorithm upon complex BEMD for the defocused images.