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

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


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.


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



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).


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Copyright information

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

Authors and Affiliations

  1. 1.Faculty of Information EngineeringGuangdong University of TechnologyGuangzhouChina

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