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=== Fast multidimensional ensemble empirical mode decomposition<ref name=":7" /> ===
For a temporal signal of length ''M'', the complexity of cubic spline sifting through its local extrema is about the order of ''M,'' and so is that of the EEMD as it only repeats the spline fitting operation with a number that is not dependent on ''M''. However, as the sifting number (often selected as 10) and the ensemble number (often a few hundred) multiply to the spline sifting operations, hence the EEMD is time consuming compared with many other time series analysis methods such as Fourier Transformstransforms and Waveletwavelet Transformstransforms.The MEEMD employs EEMD decomposition of the time serie s at each division grids of the initial temporal signal, the EEMD operation is repeated by the number of total grid points of the ___domain. The idea of the fast MEEMD is very simple. As PCA/EOF-based compression expressed the original data in terms of pairs of PCs and EOFs, through decomposing PCs, instead of time series of each grid, and using the corresponding spatial structure depicted by the corresponding EOFs, the computational burden can be significantly reduced.
The fast MEEMD includes the following steps:
# All pairs of EOF's, Vi''V''<sub>''i''</sub>, and their corresponding PCs, Yi''Y''<sub>''i''</sub>, of Spatiospatio-Temporaltemporal data over a compressed sub-___domain are computed.
# The number of pairs of PC/EOF that are retained in the compressed data is determined by the calculation of the accumulated total variance of leading EOF/PC pairs.
# Each PC Yi''Y''<sub>''i''</sub> is decomposed using EEMD, i.e.
::: <math>Y_i=\sum_{j=1}^nc_{j,i}+r_{n,i}</math><ref name=":7" />
where ''c(''<sub>''j'',''i)''</sub> represents simple oscillatory modes of certain frequencies and ''r(''<sub>''n'',''i)''</sub> is the residual of the data Yi''Y''<sub>''i''</sub>. The result of the ith''i''th MEEMD component Cj''C''<sub>''j''</sub> is obtained as <math>C_j=\sum_{j=1}^{40} c_{j,i} V_i</math>.<ref name=":7" />
In this compressed computation, we have used the approximate dyadic filter bank properties of EMD/EEMD.
Note that Aa detailed knowledge of the Intrinsicintrinsic mode functions of a noise corrupted signal can help in estimating the significance of that mode. It is usually assumed that the first IMF captures most of the noise and hence from this IMF we could estimate the Noise level and estimate the noise corrupted signal eliminating the effects of noise approximately. This method is known as Denoisingdenoising and Detrendingdetrending. Another advantage of using the MEEMD is that the mode mixing is reduced significantly due to the function of the EEMD.<br />The Denoisingdenoising and Detrendingdetrending strategy can be used for image processing to enhance an image and similarly it could be applied to Audio Signals to remove corrupted data in speech. The MDEEMD could be used to break down images and audio signals into IMF and based on the knowledge of the IMF perform necessary operations. The decomposition of an image is very advantageous for Radar-based application the decomposition of an image could reveal land mines etc.
== Parallel implementation of multi-dimensional ensemble empirical mode decomposition.<ref name=":8" /> ==
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