Warianty tytułu
Języki publikacji
Abstrakty
Empirical mode decomposition (EMD) is a popular, user-friendly, data-driven algorithm to decompose a given (non-stationary) signal into its constituting components, utilizing spline interpolation. This algorithm was first proposed in 1998 in the one-dimensional setting, and it employed standard cubic spline interpolation. Since then, different two-dimensional extensions of EMD have been proposed. In this paper, we consider one of these two-dimensional extensions and adapt it to use a shape-preserving interpolation scheme based on quadratic B-splines, ensuring that monotonicity and concavity in the input data are preserved. Using multiple numerical experiments, we show that this new scheme outperforms the original EMD, both qualitatively and quantitatively.
Czasopismo
Rocznik
Tom
Strony
287--296
Opis fizyczny
Bibliogr. 15 poz., il. kolor., 1 fot., wykr.
Twórcy
autor
- Department of Mathematics and Computer Science, Westmont College, Santa Barbara, CA 93108, USA, webrown@westmont.edu
autor
- Department of Mathematics and Computer Science, Westmont College, Santa Barbara, CA 93108, USA, mvanderwalt@westmont.edu
Bibliografia
- [1] C.-S. Chen and Y. Jeng, Two-dimensional nonlinear geophysical data filtering using the multidimensional EEMD method, J. Appl. Geophys. 111 (2014), 256-270.
- [2] W.-K. Chen, J.-C. Lee, W.-Y. Han, C.-K. Shih and K.-C. Chang, Iris recognition based on bidimensional empirical mode decomposition and fractal dimension, Inform. Sci. 221 (2013), 439-451.
- [3] C. K. Chui and M. D. van der Walt, Signal analysis via instantaneous frequency estimation of signal components, Int. J. Geomath. 6 (2015), 1-42.
- [4] Z.-P. Fan and G.-L. Zhang, The research of improved envelope algorithm of EMD, Comput. Simul. 27 (2010), no. 6, 126-129.
- [5] N. E. Huang, M.-L. C. Wu, S. R. Long, S. S. P. Shen, W.g Qu, P. Gloersen and K. L. Fan, A confidence limit for the empirical mode decomposition and Hilbert spectral analysis, Proc. Roy. Soc. Lond. Ser A 459 (2003), no. 2037, 2317-2345.
- [6] N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung and H. H. Liu, The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, Proc. Roy. Soc. Lond. Ser A 454 (1998), no. 1971, 903-995.
- [7] N. E. Huang and Z. Wu, A review on Hilbert-Huang transform: Method and its applications to geophysical studies, Rev. Geophys. 46 (2008), DOI 10.1029/2007RG000228.
- [8] Y. Li, M. Xu, Y. Wei and W. Huang, An improvement EMD method based on the optimized rational hermite interpolation approach and its application to gear fault diagnosis, Measurement 63 (2015), 330-345.
- [9] J. C. Nunes, S. Guyot and E. Deléchelle, Texture analysis based on local analysis of the bidimensional empirical mode decomposition, Machine Vis. Appl. 16 (2005), no. 3, 177-188.
- [10] X. Qin, S. Liu, Z. Wu and H. Jun, Medical image enhancement method based on 2d empirical mode decomposition, in: 2nd International Conference on Bioinformatics and Biomedical Engineering, IEEE Press, Piscataway (2008), 2533-2536.
- [11] L. Schumaker, On shape preserving quadratic spline interpolation, SIAM J. Numer. Anal. 20 (1983), no. 4, 854-864.
- [12] S. Sinclair and G. G. S. Pegram, Empirical mode decomposition in 2-d space and time: A tool for space-time rainfall analysis and nowcasting, Hydrol. Earth Syst. Sci. 9 (2005), no. 3, 127-137.
- [13] M. D. van der Walt, Empirical mode decomposition with shape-preserving spline interpolation, Results Appl. Math. 5 (2020), Article ID 100086.
- [14] Z. Wu, N. E. Huang and X. Chen, The multi-dimensional ensemble empirical mode decomposition method, Adv. Adaptive Data Anal. 1 (2009), no. 3, 339-372.
- [15] Y. Xu, B. Liu, J. Liu and S. Riemenschneider, Two-dimensional empirical mode decomposition by finite elements, Proc. Roy. Soc. A 462 (2006), no. 2074, 3081-3096.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-769e96f1-9092-431c-9ad8-d681ade9e42b