Generalized phase space projection for nonlinear noise reduction

Michael T. Johnson, Richard J. Povinelli

Research output: Contribution to journalArticlepeer-review

46 Scopus citations


Improved phase space projection methods, adapted from related work in the linear signal processing field based on subspace decomposition, are presented for application to the problem of additive noise reduction in the context of phase space analysis. These methods improve upon existing methods such as Broomhead-King singular spectrum analysis projection by minimizing overall signal distortion subject to constraints on the residual error, rather than using a direct least-squares fit. This results in a range of weighted projections which estimate and compensate for the portion of the principal component's singular values corresponding to noise rather than signal energy, and which include least-squares (LS) and least minimum mean square error (LMMSE) as subcases. The nature of phase space covariance, the key element in construction of the projection matrix, is examined across global phase spaces as well as within local neighborhood regions. The resulting algorithm, illustrated on a noisy Henon map as well as on the task of speech enhancement, is applicable to a wide variety of nonlinear noise reduction tasks.

Original languageEnglish
Pages (from-to)306-317
Number of pages12
JournalPhysica D: Nonlinear Phenomena
Issue number3-4
StatePublished - Feb 15 2005


  • Noise reduction
  • Singular spectrum analysis
  • Subspace decomposition

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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