An adaptive way for improving noise reduction using local geometric projection

Alexandras Leontitsis, Tassos Bountis, Jenny Pagge

Research output: Contribution to journalArticle

37 Citations (Scopus)

Abstract

We propose an adaptive way to improve noise reduction by local geometric projection. From the neighborhood of each candidate point in phase space, we identify the best subspace that the point will be orthogonally projected to. The signal subspace is formed by the most significant eigendirections of the neighborhood, while the less significant ones define the noise subspace. We provide a simple criterion to separate the most significant eigendirections from the less significant ones. This criterion is based on the maximum logarithmic difference between the neighborhood eigendirection lengths, and the assumption that there is at least one eigendirection that corresponds to the noise subspace. In this way, we take into account the special characteristics of each neighborhood and introduce a more successful noise reduction technique. Results are presented for a chaotic time series of the Hénon map and Ikeda map, as well as on the Nasdaq Composite index.

Original languageEnglish
Pages (from-to)106-110
Number of pages5
JournalChaos
Volume14
Issue number1
DOIs
Publication statusPublished - 2004
Externally publishedYes

Fingerprint

Noise Reduction
Noise abatement
noise reduction
projection
Subspace
Projection
Time series
Chaotic Time Series
composite materials
Composite materials
Phase Space
Logarithmic
Composite

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

Cite this

An adaptive way for improving noise reduction using local geometric projection. / Leontitsis, Alexandras; Bountis, Tassos; Pagge, Jenny.

In: Chaos, Vol. 14, No. 1, 2004, p. 106-110.

Research output: Contribution to journalArticle

Leontitsis, A, Bountis, T & Pagge, J 2004, 'An adaptive way for improving noise reduction using local geometric projection', Chaos, vol. 14, no. 1, pp. 106-110. https://doi.org/10.1063/1.1622354
Leontitsis, Alexandras ; Bountis, Tassos ; Pagge, Jenny. / An adaptive way for improving noise reduction using local geometric projection. In: Chaos. 2004 ; Vol. 14, No. 1. pp. 106-110.
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