Abstract
This paper proposes a singular spectrum analysis (SSA)-based hierarchical multiresolution analysis (HMA) with the exploitation of the frequency selectivities of the desirable grouped functions. To perform the HMA, the SSA components are grouped based on the desirable grouped functions. Similar procedures are applied to the sum of the SSA components in a group in the previous level of decomposition. Computer numerical simulation results show that the SSA components in the next level of decomposition are localized within the passband of the sum of the SSA components in the corresponding group in the previous level of decomposition if its intrinsic mode functions (IMFs) or the ideal filters are employed as the desirable grouped functions. Moreover, unlike the empirical mode decomposition (EMD)-based HMA, the total number of the SSA components in each level of decomposition can be chosen.
Similar content being viewed by others
References
M.A. Coffey, D.M.Etter, D.M., Multiresolution analysis on bounded domains for the design of biorthogonal wavelet bases. IEEE Trans. Signal Process. 50(3):509–519 (2002).
F. Flitti, C. Collet, E. Slezak, Image fusion based on pyramidal multiband multiresolution markovian analysis. Signal Image Video Process. 3, 275–289 (2009)
S.S. Gajbhar, M.V. Joshi, Design of complex adaptive multiresolution directional filter bank and application to pansharpening. Signal Image Video Process. 11, 259–266 (2017)
B. Gao, W.L. Woo, S.S. Dlay, Single-channel source separation using EMD-subband variable regularized sparse features. IEEE Trans. Audio Speech Lang. Process. 19(4), 961–972 (2011)
B. Gao, W.L. Woo, S.S. Dlay, Variational regularized 2-D nonnegative matrix factorization. IEEE Trans. Neural Netw. Learn. Syst. 23(5), 703–716 (2012)
J.M. Gauch, S.M. Pizer, Multiresolution analysis of ridges and valleys in grey-scale images. IEEE Trans. Pattern Anal. Mach. Intell. 15(6), 635–646 (1993)
P.H. Hennings-Yeomans, G.F. Cooper, Improving the prediction of clinical outcomes from genomic data using multiresolution analysis. IEEE Trans. Comput. Biol. Bioinform. 9(5), 1442–1450 (2012)
W. Kuang, Z. Yang, B.W.K. Ling, C.Y.F. Ho, Q. Dai, Nonlinear and adaptive undecimated hierarchical multiresolution analysis for real valued discrete time signals via empirical mode decomposition. Digital Signal Process. 45, 36–54 (2015)
P. Lin, W. Kuang, Y. Liu, B.W.K. Ling, Grouping and selecting singular spectrum analysis components for denoising via empirical mode decomposition approach. Circ. Syst. Signal Process. 38, 356–370 (2019)
J. Liu, P. Pillay, An insight into power quality disturbances using wavelet multiresolution analysis. IEEE Power Eng. Rev. 19(9), 59–60 (1999)
M. Masugi, Multiresolution analysis of electrostatic discharge current from electromagnetic interference aspects. IEEE Trans. Electromag. Compat. 45(2), 393–403 (2003)
P. Pirinoli, G. Vecchi, L. Matekovits, Multiresolution analysis of printed antennas and circuits: a dual-isoscalar approach. IEEE Trans. Antennas Propag. 49(6), 858–874 (2001)
J. Shi, X. Liu, N. Zhang, Multiresolution analysis and orthogonal wavelets associated with fractional wavelet transform. Signal Image Video Process. 9, 211–220 (2015)
J. Sudre, H. Yahia, O. Pont, V. Garçon, Ocean turbulent dynamics at superresolution from optimal multiresolution analysis and multiplicative cascade. IEEE Trans. Geosci. Remote Sens. 53(11), 6274–6285 (2015)
Z. Tian, B.W.K. Ling, X. Zhou, R.W.K. Lam, K.-L. Teo, Suppressing the spikes in electroencephalogram via an iterative joint singular spectrum analysis and low rank decomposition approach. Sensors 20(2), 341 (2020)
X. Wang, W. Yu, X. Qi, Y. Deng, Y. Liu, Radiofrequency interference suppression in synthetic aperture radar based on singular spectrum analysis with extended: FAPI subspace tracking. IET Radar Sonar Navig. 6(9), 881–890 (2012)
Z. Yang, B.W.K. Ling, C. Bingham, Trend extraction based on separations of consecutive empirical mode decomposition components in Hilbert marginal spectrum. Measurement 46, 2481–2491 (2013)
Z. Yang, B.W.K. Ling, C. Bingham, Joint empirical mode decomposition and sparse binary programming for underlying trend extraction. IEEE Trans. Instrum. Meas. 62(10), 2673–2682 (2013)
Acknowledgements
This paper was supported partly by the National Nature Science Foundation of China (Nos. U1701266, 61671163 and 62071128), the Team Project of the Education Ministry of the Guangdong Province (No. 2017KCXTD011), the Guangdong Higher Education Engineering Technology Research Center for Big Data on Manufacturing Knowledge Patent (No. 501130144) and Hong Kong Innovation and Technology Commission, Enterprise Support Scheme (No. S/E/070/17).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Feng, P., Ling, B.WK. Singular Spectrum Analysis-Based Hierarchical Multiresolution Analysis with Exploitation of Frequency Selectivities of Desirable Grouped Functions. Circuits Syst Signal Process 40, 2967–2981 (2021). https://doi.org/10.1007/s00034-020-01607-3
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00034-020-01607-3