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K T Osman - One of the best experts on this subject based on the ideXlab platform.

  • local anisotropy higher order Statistics and turbulence spectra
    The Astrophysical Journal, 2012
    Co-Authors: W H Matthaeus, S Servidio, P Dmitruk, V Carbone, Sean Oughton, Minping Wan, K T Osman
    Abstract:

    Correlation anisotropy emerges dynamically in magnetohydrodynamics (MHD), producing stronger gradients across the large-scale mean magnetic field than along it. This occurs both globally and locally, and has significant implications in space and astrophysical plasmas, including particle scattering and transport, and theories of turbulence. Properties of local correlation anisotropy are further documented here by showing through numerical experiments that the effect is intensified in more localized estimates of the mean field. The mathematical formulation of this property shows that local anisotropy mixes second-order with higher order correlations. Sensitivity of local statistical estimates to higher order correlations can be understood in connection with the stochastic coordinate system inherent in such formulations. We demonstrate this in specific cases, and illustrate the connection to higher order Statistics by showing the sensitivity of local anisotropy to phase randomization, after which the global measure of anisotropy is recovered at all scales of averaging. This establishes that anisotropy of the local structure function is not a measure of anisotropy of the energy spectrum. Evidently, the local enhancement of correlation anisotropy is of substantial fundamental interest and must be understood in terms of higher order correlations, specifically fourth-order and above.

  • local anisotropy higher order Statistics and turbulence spectra
    arXiv: Space Physics, 2012
    Co-Authors: W H Matthaeus, S Servidio, P Dmitruk, V Carbone, Sean Oughton, Minping Wan, K T Osman
    Abstract:

    Correlation anisotropy emerges dynamically in magnetohydrodynamics (MHD), producing stronger gradients across the large-scale mean magnetic field than along it. This occurs both globally and locally, and has significant implications in space and astrophysical plasmas, including particle scattering and transport, and theories of turbulence. Properties of local correlation anisotropy are further documented here by showing through numerical experiments that the effect is intensified in more localized estimates of the mean field. The mathematical formulation of this property shows that local anisotropy mixes second-order with higher order correlations. Sensitivity of local statistical estimates to higher order correlations can be understood in connection with the stochastic coordinate system inherent in such formulations. We demonstrate this in specific cases, illustrate the connection to higher order Statistics by showing the sensitivity of local anisotropy to phase randomization, and thus establish that the local structure function is not a measure of the energy spectrum. Evidently the local enhancement of correlation anisotropy is of substantial fundamental interest, and this phenomenon must be understood in terms of higher order correlations, fourth-order and above.

J K Tugnait - One of the best experts on this subject based on the ideXlab platform.

  • identification and deconvolution of multichannel linear non gaussian processes using higher order Statistics and inverse filter criteria
    IEEE Transactions on Signal Processing, 1997
    Co-Authors: J K Tugnait
    Abstract:

    This paper is concerned with the problem of estimation and deconvolution of the matrix impulse response function of a multiple-input multiple-output (MIMO) system given only the measurements of the vector output of the system. The system is assumed to be driven by a temporally i.i.d. and spatially independent non-Gaussian vector sequence (which is not observed). An iterative, inverse filter criteria-based approach is developed using the third-order or the fourth-order normalized cumulants of the inverse filtered data at zero lag. Stationary points of the proposed cost functions are investigated. The approach is input iterative, i.e., the input sequences are extracted and removed one by one. The matrix impulse response is then obtained by cross correlating the extracted inputs with the observed outputs. Identifiability conditions are analyzed. The strong consistency of the proposed approach is also briefly discussed. Computer simulation examples are presented to illustrate the proposed approaches.

  • estimation of linear parametric models using inverse filter criteria and higher order Statistics
    IEEE Transactions on Signal Processing, 1993
    Co-Authors: J K Tugnait
    Abstract:

    Considers the problem of estimating the parameters of a stable, scalar ARMA (p, q) signal model (causal or noncausal, minimum phase or mixed phase) driven by an i.i.d. non-Gaussian sequence. The driving noise sequence is not observed. The Wiggins-Donoho (1978, 1991) class of inverse filter criteria for estimation of model parameters are analyzed and extended. These criteria have been considered in the past only for moving average inverse filters. These criteria are extended to general ARMA inverses. Computer simulation examples are presented to illustrate the proposed approaches. >

Philippe Boulinguez - One of the best experts on this subject based on the ideXlab platform.

  • greater robustness of second order Statistics than higher order Statistics algorithms to distortions of the mixing matrix in blind source separation of human eeg implications for single subject and group analyses
    NeuroImage, 2013
    Co-Authors: Guillaume Lio, Philippe Boulinguez
    Abstract:

    A mandatory assumption in blind source separation (BSS) of the human electroencephalogram (EEG) is that the mixing matrix remains invariant, i.e., that the sources, electrodes and geometry of the head do not change during the experiment. Actually, this is not often the case. For instance, it is common that some electrodes slightly move during EEG recording. This issue is even more critical for group independent component analysis (gICA), a method of growing interest, in which only one mixing matrix is estimated for several subjects. Indeed, because of interindividual anatomo-functional variability, this method violates the mandatory principle of invariance. Here, using simulated (experiments 1 and 2) and real (experiment 3) EEG data, we test how eleven current BSS algorithms undergo distortions of the mixing matrix. We show that this usual kind of perturbation creates non-Gaussian features that are virtually added to all sources, impairing the estimation of real higher order Statistics (HOS) features of the actual sources by HOS algorithms (e.g., Ext-INFOMAX, FASTICA). HOS-based methods are likely to identify more components (with similar properties) than actual neurological sources, a problem frequently encountered by BSS users. In practice, the quality of the recovered signal and the efficiency of subsequent source localization are substantially impaired. Performing dimensionality reduction before applying HOS-based BSS does not seem to be a safe strategy to circumvent the problem. Second order Statistics (SOS)-based BSS methods belonging to the less popular SOBI family class are much less sensitive to this bias.

W H Matthaeus - One of the best experts on this subject based on the ideXlab platform.

  • local anisotropy higher order Statistics and turbulence spectra
    The Astrophysical Journal, 2012
    Co-Authors: W H Matthaeus, S Servidio, P Dmitruk, V Carbone, Sean Oughton, Minping Wan, K T Osman
    Abstract:

    Correlation anisotropy emerges dynamically in magnetohydrodynamics (MHD), producing stronger gradients across the large-scale mean magnetic field than along it. This occurs both globally and locally, and has significant implications in space and astrophysical plasmas, including particle scattering and transport, and theories of turbulence. Properties of local correlation anisotropy are further documented here by showing through numerical experiments that the effect is intensified in more localized estimates of the mean field. The mathematical formulation of this property shows that local anisotropy mixes second-order with higher order correlations. Sensitivity of local statistical estimates to higher order correlations can be understood in connection with the stochastic coordinate system inherent in such formulations. We demonstrate this in specific cases, and illustrate the connection to higher order Statistics by showing the sensitivity of local anisotropy to phase randomization, after which the global measure of anisotropy is recovered at all scales of averaging. This establishes that anisotropy of the local structure function is not a measure of anisotropy of the energy spectrum. Evidently, the local enhancement of correlation anisotropy is of substantial fundamental interest and must be understood in terms of higher order correlations, specifically fourth-order and above.

  • local anisotropy higher order Statistics and turbulence spectra
    arXiv: Space Physics, 2012
    Co-Authors: W H Matthaeus, S Servidio, P Dmitruk, V Carbone, Sean Oughton, Minping Wan, K T Osman
    Abstract:

    Correlation anisotropy emerges dynamically in magnetohydrodynamics (MHD), producing stronger gradients across the large-scale mean magnetic field than along it. This occurs both globally and locally, and has significant implications in space and astrophysical plasmas, including particle scattering and transport, and theories of turbulence. Properties of local correlation anisotropy are further documented here by showing through numerical experiments that the effect is intensified in more localized estimates of the mean field. The mathematical formulation of this property shows that local anisotropy mixes second-order with higher order correlations. Sensitivity of local statistical estimates to higher order correlations can be understood in connection with the stochastic coordinate system inherent in such formulations. We demonstrate this in specific cases, illustrate the connection to higher order Statistics by showing the sensitivity of local anisotropy to phase randomization, and thus establish that the local structure function is not a measure of the energy spectrum. Evidently the local enhancement of correlation anisotropy is of substantial fundamental interest, and this phenomenon must be understood in terms of higher order correlations, fourth-order and above.

Athina P Petropulu - One of the best experts on this subject based on the ideXlab platform.

  • frequency domain blind mimo system identification based on second and higher order Statistics
    IEEE Transactions on Signal Processing, 2001
    Co-Authors: Binning Chen, Athina P Petropulu
    Abstract:

    We present a novel frequency-domain framework for the identification of a multiple-input multiple-output (MIMO) system driven by white, mutually independent, unobservable inputs. The system frequency response is obtained based on singular value decomposition (SVD) of a matrix constructed based on the power-spectrum and slices of polyspectra of the system output. By appropriately selecting the polyspectra slices, we can create a set of such matrices, each of which could independently yield the solution, of they could all be combined in a joint diagonalization scheme to yield a solution with improved statistical performance. The freedom to select the polyspectra slices allows us to bypass the frequency-dependent permutation ambiguity that is usually associated with frequency domain SVD, while at the same time allows us compute and cancel the phase ambiguity. An asymptotic consistency analysis of the system magnitude response estimate is performed.