Advertisement

De-Hankelization of singular spectrum analysis matrices via L1 norm criterion

  • Ziyin Huang
  • Bingo Wing-Kuen LingEmail author
Original Paper
  • 6 Downloads

Abstract

This paper proposes to employ the L1 norm criterion to perform the de-Hankelization in the singular spectrum analysis (SSA). In particular, the represented values of the off-diagonals in the two-dimensional SSA matrices are found via minimizing the L1 norm errors of the vectors defining as the absolute differences between the off-diagonal vectors and the vectors with all their elements being the represented values. This results to reduce the total number of the large-valued elements in the error vectors. Also, this paper guarantees to achieve the exact perfect reconstruction of the original signal. As the formulated problem is a standard linear programming problem, the solution could be efficiently found via the simplex method. The computer numerical simulations verify the results.

Keywords

Singular Spectrum analysis De-Hankelization L1 norm criterion Exact perfect reconstruction condition 

Notes

Acknowledgements

This paper is supported partly by the National Nature Science Foundation of China (Nos. U1701266, 61372173, 61471132 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), the Science and Technology Planning Project of Guangdong Province China (No. 2015A030401090) and Enterprise Support Scheme, ITC Hong Kong SAR (S/E070/17).

References

  1. 1.
    Lin, P.-R., Li, W., Zheng, T., Ling, W.-K., Li, C.-K.: Information extraction via singular spectrum analysis for noninvasive blood glucose estimation system inspired by empirical mode decomposition. In: International conference on industrial informatics, INDIN, pp. 18–21 (2016)Google Scholar
  2. 2.
    Torkamani-Azar, F., Parkkinen, J.: Image quality assessment using block-based weighted SVD. Signal Image Video Process. 12, 1337–1344 (2018)CrossRefGoogle Scholar
  3. 3.
    Zabalza, J., Ren, J., Wang, Z., Marshall, S., Wang, J.: Singular spectrum analysis for effective feature extraction in hyperspectral imaging. IEEE Geosci. Remote Sens. Lett. 11(11), 1886–1890 (2014)CrossRefGoogle Scholar
  4. 4.
    Ji, H., Li, Y., Dong, E., Xue, P., Xiong, W., Sun, W., Tang, Z., Zhang, D., Fang, W.: A non-rigid image registration method based on multi-level B-spline and L 2-regularization. Signal Image Video Process. 12, 1217–1225 (2018)CrossRefGoogle Scholar
  5. 5.
    Ramirez, C., Argaez, M.: An l1 minimization algorithm for non-smooth regularization in image processing. Signal Image Video Process. 9, 373–386 (2015)CrossRefGoogle Scholar
  6. 6.
    Shi, L., Zhao, H.: L 1-norm constrained normalized subband adaptive filter algorithm with variable norm-bound parameter and improved version. Signal Image Video Process. 11, 865–871 (2017)CrossRefGoogle Scholar
  7. 7.
    Li, Ya., Ling, B.W.-K., Xie, L., Dai, Q.: Using LASSO for formulating constraint of least-squares programming for solving one-norm equality constrained problem. Signal Image Video Process. 11, 179–186 (2017)CrossRefGoogle Scholar
  8. 8.
    Huang, Z., Gu, J., Ling, W.-K.: De-Hankelization of singular spectrum analysis matrices via an optimization approach for blood glucose estimation. In: International conference on consumer electronics China, ICCE-China (2016)Google Scholar
  9. 9.
    Golyandina, N.E., Nekrutkin, V.V., Zhigljavsky, A.A.: Analysis of Time Series Structure: SSA and Related Techniques. Chapman and Hall/CRC, Boca Raton (2001)CrossRefzbMATHGoogle Scholar
  10. 10.
    Elsner, J.B., Tsonis, A.A.: Singular Spectrum Analysis: A New Tool in Time Series Analysis. Springer, Berlin (1996)CrossRefGoogle Scholar
  11. 11.
    Touil, I., Benterki, D., Yassine, A.: A feasible primal-dual interior point method for linear semidefinite programming. J. Comput. Appl. Math. 312, 216–230 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Wu, Z.W., Yao, M.L., Ma, H.G., Jia, W.M.: De-noising MEMS inertial sensors for low-cost vehicular attitude estimation based on singular spectrum analysis and independent component analysis. Electron. Lett. 49, 892–893 (2013)CrossRefGoogle Scholar
  13. 13.
    Wang, R., Man, H.G., Liu, G.Q., Zuo, D.G.: Selection of window length for singular spectrum analysis. J. Frankl. Inst. 352, 1541–1560 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Yang, Z., Ling, B. W.-K., Bingham, C.: Extracting underlying trend and predicting power usage via joint SSA and sparse binary programming. In: International symposium on circuits and systems, ISCAS, pp. 19–23 (2013)Google Scholar
  15. 15.
    Harmouche, J., Fourer, D., Auger, F., Borgnat, P., Flandrin, P.: The sliding singular spectrum analysis: a data-driven nonstationary signal decomposition tool. IEEE Trans. Signal Process. 16(1), 251–263 (2018)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of Information EngineeringGuangdong University of TechnologyGuangzhouChina

Personalised recommendations