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Properties of approximated empirical mode decomposition and optimal design of its system kernel matrix for signal decomposition

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Abstract

An approximated empirical mode decomposition generates a set of approximated intrinsic mode functions via a linear, nonadaptive but iterative approach. The decomposition was found to be very useful for a content-independent pattern recognition application. As the process is characterized by a system kernel matrix and performed iteratively, the approximated intrinsic mode functions can be understood as the original signals processed by a set of mask operations. Here, some properties of the decomposition are studied and an optimal design of the system kernel matrix is proposed. It is found that there is only one approximated intrinsic mode function if the exact perfect reconstruction condition is satisfied. Obviously, the approximated intrinsic mode function is the original signal. Therefore, the decomposition is practically not meaningful. To address this issue, the infinite number of iterations in the algorithm is truncated to a finite number of iterations. Also, the design of the system kernel matrix is formulated as an optimization problem. In particular, the exact perfect reconstruction error between the sum of the approximated intrinsic mode functions and the original signal is minimized and the total absolute sum of the difference between any two different eigenvalues of the iterative matrix is maximized subject to a stability condition. Here, the stability condition refers to the eigenvalues of the iterative matrix being between zero and one. Since the optimization problem is nonsmooth and nonconvex, a genetic algorithm is employed for finding its near global optimal solution. Compared to the conventional approximated empirical mode decomposition, computer numerical simulations show that our proposed approach can achieve more than one approximated intrinsic mode function with each approximated intrinsic mode function corresponding to an output of a more meaningful mask operation.

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References

  1. Qin, Y., Tang, B., Mao, Y.: Adaptive signal decomposition based on wavelet ridge and its application. Signal Process. 120, 480–494 (2016)

    Article  Google Scholar 

  2. Jianlou, X., Feng, X., Hao, Y., Han, Yu.: Image decomposition using adaptive second-order total generalized variation. SIViP 8(1), 39–41 (2014)

    Article  Google Scholar 

  3. Kuang, W., Ling, B.W.K., Yang, Z.: Parameter free and reliable signal denoising based on constants obtained from IMFs of white Gaussian noise. Measurement 102, 230–243 (2017)

    Article  Google Scholar 

  4. Yang, Z., Ling, B.W.K., Bingham, C.: Joint empirical mode decomposition and sparse binary programming for underlying trend extraction. IEEE Trans. Instrum. Meas. 62(10), 2673–2682 (2013)

    Article  Google Scholar 

  5. Hughes, J.M., Mao, D., Rockmore, D.N., Wang, Y., Qiang, W.: Empirical mode decomposition analysis for visual stylometry. IEEE Trans. Pattern Anal. Mach. Intell. 34(11), 2147–2157 (2012)

    Article  Google Scholar 

  6. Gao, B., Woo, W.-L., Dlay, S.S.: Variational regularized 2-D nonnegative matrix factorization. IEEE Trans. Neural Netw. Learn. Syst. 23(5), 703–716 (2012)

    Article  Google Scholar 

  7. Ling, B.W.K., Tian, N., Ho, C.Y.F., Siu, W.C., Teo, K.L., Dai, Q.: Maximally decimated paraunitary linear phase FIR filter bank design via iterative SVD approach. IEEE Trans. Signal Process. 63(2), 466–481 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  8. Ling, B.W.K., Ho, C.Y.F., Teo, K.L., Siu, W.C., Cao, J., Dai, Q.: Optimal design of cosine modulated nonuniform linear phase FIR filter bank via both stretching and shifting frequency response of single prototype filter”. IEEE Trans. Signal Process. 62(10), 2517–2530 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  9. Huang, N.E., Wu, M.L.C., Long, S.R., Shen, S.S., Qu, W., Gloersen, P., Fan, K.L.: A confidence limit for the empirical mode decomposition and Hilbert spectral analysis. Proc. R. Soc. Lond. Ser. A 459(2037), 2317–2345 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  10. Gao, B., Woo, W.-L., Dlay, S.S.: Single, channel blind source separation using EMD-subband variable regularized sparse features”. IEEE Trans. Audio Speech Lang. Process. 19(4), 961–976 (2011)

    Article  Google Scholar 

  11. Gupta, R., Kumar, A., Bahl, R.: Estimation of instantaneous frequencies using iterative empirical mode decomposition. SIViP 8(5), 799–812 (2014)

    Article  Google Scholar 

  12. Lin, L., Yang, Y., Zhou, H.: Iterative filtering as an alternative algorithm for empirical mode decomposition. Adv. Adapt. Data Anal. 1(4), 543–560 (2009)

    Article  MathSciNet  Google Scholar 

  13. Khatami, L.: The poset of the nilpotent commutator of a nilpotent matrix. Linear Algebra Appl. 439(12), 3763–3776 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  14. Farokhi, S., Shamsuddin, S.M., Sheikh, U.U., Flusser, J., Khansari, M., Jafari-Khouzani, K.: Near infrared face recognition by combining Zernike moments and undecimated discreet wavelet transform. Digit. Signal Process. 31, 13–27 (2014)

    Article  Google Scholar 

  15. Ling, B.W.K., Xie, L., Cao, J., Dai, Q.: Using LASSO for formulating constraint of least-squares programming for solving one norm equality constrained problem. SIViP 11, 179–186 (2017)

    Article  Google Scholar 

  16. Ho, C.Y.F., Ling, B.W.K., Benmesbah, L., Kok, T.C.W., Siu, W.C., Teo, K.L.: Two-channel linear phase FIR QMF bank minimax design via global nonconvex optimization programming. IEEE Trans. Signal Process. 58(8), 4436–4441 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  17. Ma, B., Xia, Y.: A tribe competition-based genetic algorithm for feature selection in pattern classification. Appl. Soft Comput. 58, 328–338 (2017)

    Article  Google Scholar 

Download references

Acknowledgements

This paper is supported partly by the National Nature Science Foundation of China (Nos. U1701266, 61372173 and 61671163), the Guangdong Higher Education Engineering Technology Research Center for Big Data on Manufacturing Knowledge Patent (No. 501130144), the Natural Science Foundation of Guangdong Province China (No. 2014A030310346) and the Science and Technology Planning Project of Guangdong Province China (No. 2015A030401090).

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Authors and Affiliations

  1. Guangzhou Higher Education Mega Center, School of Information Engineering, Guangdong University of Technology, No. 100, Waihuan Xi Road, Guangzhou, Guangdong Province, China

    Nili Tian, Xiaoling Wang & Bingo Wing-Kuen Ling

  2. CSE Eng, Marmara University, Istanbul, Turkey

    Mustafa Sakalli

Authors
  1. Nili Tian
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  2. Xiaoling Wang
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  3. Bingo Wing-Kuen Ling
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  4. Mustafa Sakalli
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Correspondence to Bingo Wing-Kuen Ling.

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Tian, N., Wang, X., Ling, B.WK. et al. Properties of approximated empirical mode decomposition and optimal design of its system kernel matrix for signal decomposition. SIViP 13, 1173–1181 (2019). https://doi.org/10.1007/s11760-019-01461-0

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  • DOI: https://doi.org/10.1007/s11760-019-01461-0

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