De-Hankelization of singular spectrum analysis matrices via L 1 norm criterion

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.

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