Perfect reconstructable decimated two-dimensional empirical mode decomposition filter banks

Traditional two-dimensional empirical mode decomposition (2D-EMD) algorithms generate multiple subband signals, each having the same size of the original signal. Thus, huge amounts of data to be stored may be generated. Moreover, the computational load is massive as the decomposition levels increase. This paper introduces a method to reduce the data generated (i.e. reduce storage requirement) by incorporating decimation into the 2D-EMD, while maintaining perfect reconstruction. Furthermore, it is well established that traditional EMDs can be thought as having the structure of a single dyadic filter bank. The proposed algorithm is applicable into any arbitrary tree structures including octave filter banks, 2D-EMD packets when applied to a full binary tree, etc. The methodology hereby presented builds on the algorithm introduced by the authors in [8].