Abstract
The Bidimensional Empirical Mode Decomposition (BEMD) has taken its place among the most known decomposition methods as Fourier transform and wavelet, but the enormous execution time that it requires represents a real obstacle for its application. Hence the Fast and Adaptive Bidimensional Empirical Mode Decomposition (FABEMD) is proposed basically to overcome this obstacle by decreasing the execution time of the BEMD; its principle is based on the use of statistical filters to generate the upper and the lower envelopes instead of the interpolation functions used in the BEMD. In this work we propose a 3D extension of the FABEMD denoted Fast and Adaptive Tridimensional Empirical Mode Decomposition which can decompose a volume into a set of Tridimensional Intrinsic Mode Functions (TIMFs), the first TIMFs belong to the high frequencies and the last ones to the low frequencies. The proposed approach takes an efficient runtime compared with the considerable one required by the Multidimensional Ensemble Empirical Mode Decomposition, and it ensures a good quality of the decomposition in term of orthogonality and reconstruction. The obtained results are encouraging and will open a new road to three dimensional extensions of many applications.
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References
Aherrahrou, N., & Tairi, H. (2012) An improved images watermarking scheme using FABEMD decomposition and DCT. In Image and signal processing (pp. 307–315). Springer, Berlin.
Ahmed, M. U., & Mandic, D. P. (2010). Image fusion based on fast and adaptive bidimensional empirical mode decomposition. In IEEE 13th conference on information fusion, Fusion 2010 (pp. 1–6).
Bhuiyan, S. M. A., Adhami, R. R., & Khan, J. F. (2008). Fast and adaptive bidimensional empirical mode decomposition using order-statistics filter based envelope estimation. EURASIP Journal on Advances in Signal Processing. doi:10.1155/2008/728356.
Cheng, J., Yu, D., & Yang, Y. (2006). Research on the intrinsic mode function (IMF) criterion in EMD method. Mechanical Systems and Signal Processing, 20, 817–824.
Coughlin, K. T., & Tung, K. K. (2004). 11-Year solar cycle in the stratosphere extracted by the empirical mode decomposition method. Advances in Space Research, 34(2), 323–329.
Damerval, C., Meignen, S., & Perrier, V. (2005). A fast algorithm for bidimensional EMD. IEEE Signal Processing Letters, 12(10), 701–704.
Fitzpatrick, J. (1997). Retrospective image registration and evaluation project (RIRE) http://www.insight-journal.org/rire/index.php.
Fleureau, J., Kachenoura, A., Albera, L., Nunes, J.-C., & Senhadji, L. (2011). Multivariate empirical mode decomposition and application to multichannel filtering. Signal Processing, 91, 2783–2792.
Hualou, L., Qiu-Hua, L., & Chen, J. (2005). Application of the empirical mode decomposition to the analysis of esophageal manometric data in gastroesophageal reflux disease. IEEE Transactions on Biomedical Engineering, 52(10), 620–623.
Huang, N. E., Shen, Z., Long, S. R., Wu, M. L., Shih, H. H., Zheng, Q., et al. (1998a). The empirical mode decomposition and Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society of London. Series A, 545, 903–995.
Huang, W., Shen, Z., Huang, N. E., & Fung, Y. C. (1998b). Engineering analysis of biological variables: an example of blood pressure over 1 day. Proceedings of the National Academy of Sciences of the United States of America, 95, 4816–4821.
Linderhed, A. (2004). Image compression based on empirical mode decomposition. In Proceedings of SSAB symposium image analysis (pp. 110–113). Uppsala.
Mahraz, M. A., Riffi, J., & Tairi, H. (2012). Motion estimation using the fast and adaptive bidimensional empirical mode decomposition. Journal of Real-Time Image Processing. doi:10.1007/s11554-012-0259-4.
Nunes, J. C., Bouaoune, Y., Delechelle, E., et al. (2003). Image analysis by bidimensional empirical mode decomposition. Image and Vision Computing, 21(12), 1019–1026.
Riffi, J., Mahraz, A. M., & Tairi, H. (2013). Medical image registration based on fast and adaptive bidimensional empirical mode decomposition. IET Image Processing, 7(6), 567–574.
Wang, Z., Bovik, A. C., Sheikh, H. R., et al. (2004). Image quality assessment: From error visibility to structural similarity. Image Processing, IEEE Transactions on, 13(4), 600–612.
Wu, Z., & Huang, N. E. (2009). Ensemble empirical mode decomposition: A noise-assisted data analysis method. Advances in Adaptive Data Analysis, 1(01), 1–41.
Wu, Z., Huang, N. E., & Chen, X. (2009). The multi-dimensional ensemble empirical mode decomposition method. Advances in Adaptive Data Analysis, 1(03), 339–372.
Xu, Y., Liu, B., Liu, J., & Riemenschneider, S. (2006). Two-dimensional empirical mode decomposition by finite elements. Proceedings of the Royal Society A, 462(2074), 3081–3096.
Yang, Z., Qi, D., & Yang, L. (2004). Signal period analysis based on Hilbert-Huang transform and its application to texture analysis. In Proceedings international conference on image and graphics. Hong Kong.
Zhang, R., Ma, S., Safak, E., & Hartzell, S. (2003). Hilbert-Huang transform analysis of dynamic and earthquake motion recordings. Journal of Engineering Mechanics, 129(8), 861–875.
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Riffi, J., Mahraz, A.M., Abbad, A. et al. 3D extension of the fast and adaptive bidimensional empirical mode decomposition. Multidim Syst Sign Process 26, 823–834 (2015). https://doi.org/10.1007/s11045-014-0283-6
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DOI: https://doi.org/10.1007/s11045-014-0283-6