Biomedical subjects

Rainer Hegger

Publications and source records attributed to Rainer Hegger.

4 recordsLinked to original sources

PubMed2002

Optimizing of recurrence plots for noise reduction.

We propose a way to automatically detect the best neighborhood size for a local projective noise reduction filter, where a typical problem is the proper identification of the noise level. Here we make use of concepts from the recurrence quantification analysis in order to adaptively tune the filter along the incoming time series. We define an index, to be computed via recurrence plots, whose minimum gives a clear indication of the best size of the neighborhood in the embedding space. Comparison of the local projective noise reduction filter using this optimization scheme with the state of the art is also provided.

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PubMed1999

Practical implementation of nonlinear time series methods: The TISEAN package.

We describe the implementation of methods of nonlinear time series analysis which are based on the paradigm of deterministic chaos. A variety of algorithms for data representation, prediction, noise reduction, dimension and Lyapunov estimation, and nonlinearity testing are discussed with particular emphasis on issues of implementation and choice of parameters. Computer programs that implement the resulting strategies are publicly available as the TISEAN software package. The use of each algorithm will be illustrated with a typical application. As to the theoretical background, we will essentially give pointers to the literature. (c) 1999 American Institute of Physics.

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PubMed1998

Dynamical properties of a ferroelectric capacitor observed through nonlinear time series analysis.

By data analysis the ordinary differential equation for the description of an experimental electric resonance circuit with nonlinear capacitor is derived. Triglycine sulfate (TGS) was used as nonlinear dielectric material. This is the most thoroughly investigated ferroelectric with a second order phase transition. Its static dielectric small signal behavior is well described in the framework of the Landau theory, yielding a Duffing-type ordinary differential equation as a model equation of the circuit. Data analysis allows us to check carefully the validity of this model and to determine required corrections of this simplified equation. (c) 1998 American Institute of Physics.

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PubMed1993

On noise reduction methods for chaotic data.

Recently proposed noise reduction methods for nonlinear chaotic time sequences with additive noise are analyzed and generalized. All these methods have in common that they work iteratively, and that in each step of the iteration the noise is suppressed by requiring locally linear relations among the delay coordinates, i.e., by moving the delay vectors towards some smooth manifold. The different methods can be compared unambiguously in the case of strictly hyperbolic systems corrupted by measurement noise of infinitesimally low level. It was found that all proposed methods converge in this ideal case, but not equally fast. Different problems arise if the system is not hyperbolic, and at higher noise levels. A new scheme which seems to avoid most of these problems is proposed and tested, and seems to give the best noise reduction so far. Moreover, large improvements are possible within the new scheme and the previous schemes if their parameters are not kept fixed during the iteration, and if corrections are included which take into account the curvature of the attracting manifold. Finally, the fact that comparison with simple low-pass filters tends to overestimate the relative achievements of these nonlinear noise reduction schemes is stressed, and it is suggested that they should be compared to Wiener-type filters.

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