De-Hankelization of Singular Spectrum Analysis Matrices via L1 Norm Criterion

Huang, Ziyin; Ling, Bingo Wing‐Kuen; Gu, Jialiang; Liu, Yuwei; Huang, Yicong; Li, Chi Kong

doi:10.1109/icdsp.2018.8631664

Cited by 1 publication

(1 citation statement)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These average values of these off-diagonals of each two dimensional singular spectrum analysis matrix from the elements of each one dimensional singular spectrum analysis vector [13]- [15]. Likewise, the norm approach is proposed to determine the elements of the one dimensional singular spectrum analysis vectors [11]. However, the lengths of these one dimensional singular spectrum analysis vectors are shorter than that of the original signal if the rows of the trajectory matrix are the polyphase components of the original signal.…”

Section: Introductionmentioning

confidence: 99%

Length Reduction of Singular Spectrum Analysis With Guarantee Exact Perfect Reconstruction via Block Sliding Approach

Wang

Ling

2020

IEEE Access

Self Cite

View full text Add to dashboard Cite

The conventional singular spectrum analysis is to divide a signal into segments where there is only one non-overlapping point between two consecutive segments. By putting these segments into the columns of a matrix and performing the singular value decomposition on the matrix, various one dimensional singular spectrum analysis vectors are obtained. Since different one dimensional singular spectrum analysis vectors represent different parts of the signal such as the trend part, the oscillation part and the noise part of the signal, the singular spectrum analysis plays a very important role in the nonlinear and adaptive signal analysis. However, as the length of each one dimensional singular spectrum analysis vector is the same as that of the original signal, there is a redundancy among these one dimensional singular spectrum analysis vectors. In order to reduce the required computational power and the required units for the memory storage for performing the singular spectrum analysis, this paper proposes a method to reduce the total number of the elements of all the one dimensional singular spectrum analysis vectors. In particular, the length of the shift block for generating the trajectory matrix is increased from one to a positive integer greater than one under a certain criterion. In this case, the total number of the columns of the trajectory matrix is reduced. As a result, the total number of the off-diagonals of all the two dimensional singular spectrum analysis matrices is reduced. Hence, the total number of the elements of all the one dimensional singular spectrum analysis vectors is reduced. In order to guarantee exact perfect reconstruction, this paper reformulates the de-Hankelization process. In particular, the first element of the off-diagonals of all the two dimensional singular spectrum analysis matrices is taken as the elements of the one dimensional singular spectrum analysis vectors. Exact perfect reconstruction condition is derived. Simulations show that exact perfect reconstruction can be achieved while the total number of the elements of all the one dimensional singular spectrum analysis vectors is significantly reduced.

show abstract

Section: Introductionmentioning

confidence: 99%