6,263 research outputs found
Wavelet q-Fisher Information for Scaling Signal Analysis
This article first introduces the concept of wavelet q-Fisher information and then derives a closed-form expression of this quantifier for scaling signals of parameter α. It is shown that this information measure appropriately describes the complexities of scaling signals and provides further analysis flexibility with the parameter q. In the limit of q→1, wavelet q-Fisher information reduces to the standard wavelet Fisher information and for q > 2 it reverses its behavior. Experimental results on synthesized fGn signals validates the level-shift detection capabilities of wavelet q-Fisher information. A comparative study also shows that wavelet q-Fisher information locates structural changes in correlated and anti-correlated fGn signals in a way comparable with standard breakpoint location techniques but at a fraction of the time. Finally, the application of this quantifier to H.263 encoded video signals is presented.Consejo Nacional de Ciencia y TecnologíaFOMIX-COQCY
Enabling high confidence detections of gravitational-wave bursts
With the advanced LIGO and Virgo detectors taking observations the detection
of gravitational waves is expected within the next few years. Extracting
astrophysical information from gravitational wave detections is a well-posed
problem and thoroughly studied when detailed models for the waveforms are
available. However, one motivation for the field of gravitational wave
astronomy is the potential for new discoveries. Recognizing and characterizing
unanticipated signals requires data analysis techniques which do not depend on
theoretical predictions for the gravitational waveform. Past searches for
short-duration un-modeled gravitational wave signals have been hampered by
transient noise artifacts, or "glitches," in the detectors. In some cases, even
high signal-to-noise simulated astrophysical signals have proven difficult to
distinguish from glitches, so that essentially any plausible signal could be
detected with at most 2-3 level confidence. We have put forth the
BayesWave algorithm to differentiate between generic gravitational wave
transients and glitches, and to provide robust waveform reconstruction and
characterization of the astrophysical signals. Here we study BayesWave's
capabilities for rejecting glitches while assigning high confidence to
detection candidates through analytic approximations to the Bayesian evidence.
Analytic results are tested with numerical experiments by adding simulated
gravitational wave transient signals to LIGO data collected between 2009 and
2010 and found to be in good agreement.Comment: 15 pages, 6 figures, submitted to PR
Wavelet-Based Entropy Measures to Characterize Two-Dimensional Fractional Brownian Fields
The aim of this work was to extend the results of Perez et al. (Physica A (2006), 365 (2), 282–288) to the two-dimensional (2D) fractional Brownian field. In particular, we defined Shannon entropy using the wavelet spectrum from which the Hurst exponent is estimated by the regression of the logarithm of the square coefficients over the levels of resolutions. Using the same methodology. we also defined two other entropies in 2D: Tsallis and the Rényi entropies. A simulation study was performed for showing the ability of the method to characterize 2D (in this case, α = 2) self-similar processes
The performance of spherical wavelets to detect non-Gaussianity in the CMB sky
We investigate the performance of spherical wavelets in discriminating
between standard inflationary models (Gaussian) and non-Gaussian models. For
the later we consider small perturbations of the Gaussian model in which an
artificially specified skewness or kurtosis is introduced through the Edgeworth
expansion. By combining all the information present in all the wavelet scales
with the Fisher discriminant, we find that the spherical Mexican Hat wavelets
are clearly superior to the spherical Haar wavelets. The former can detect
levels of the skewness and kurtosis of ~1% for 33' resolution, an order of
magnitude smaller than the later. Also, as expected, both wavelets are better
for discriminating between the models than the direct consideration of moments
of the temperature maps. The introduction of instrumental white noise in the
maps, S/N=1, does not change the main results of this paper.Comment: 12 pages, 7 figures, accepted by MNRAS with minor change
Multiresolution analysis in statistical mechanics. I. Using wavelets to calculate thermodynamic properties
The wavelet transform, a family of orthonormal bases, is introduced as a
technique for performing multiresolution analysis in statistical mechanics. The
wavelet transform is a hierarchical technique designed to separate data sets
into sets representing local averages and local differences. Although
one-to-one transformations of data sets are possible, the advantage of the
wavelet transform is as an approximation scheme for the efficient calculation
of thermodynamic and ensemble properties. Even under the most drastic of
approximations, the resulting errors in the values obtained for average
absolute magnetization, free energy, and heat capacity are on the order of 10%,
with a corresponding computational efficiency gain of two orders of magnitude
for a system such as a Ising lattice. In addition, the errors in
the results tend toward zero in the neighborhood of fixed points, as determined
by renormalization group theory.Comment: 13 pages plus 7 figures (PNG
Quantitative features of multifractal subtleties in time series
Based on the Multifractal Detrended Fluctuation Analysis (MFDFA) and on the
Wavelet Transform Modulus Maxima (WTMM) methods we investigate the origin of
multifractality in the time series. Series fluctuating according to a qGaussian
distribution, both uncorrelated and correlated in time, are used. For the
uncorrelated series at the border (q=5/3) between the Gaussian and the Levy
basins of attraction asymptotically we find a phase-like transition between
monofractal and bifractal characteristics. This indicates that these may solely
be the specific nonlinear temporal correlations that organize the series into a
genuine multifractal hierarchy. For analyzing various features of
multifractality due to such correlations, we use the model series generated
from the binomial cascade as well as empirical series. Then, within the
temporal ranges of well developed power-law correlations we find a fast
convergence in all multifractal measures. Besides of its practical significance
this fact may reflect another manifestation of a conjectured q-generalized
Central Limit Theorem
Detecting single-trial EEG evoked potential using a wavelet domain linear mixed model: application to error potentials classification
Objective. The main goal of this work is to develop a model for multi-sensor
signals such as MEG or EEG signals, that accounts for the inter-trial
variability, suitable for corresponding binary classification problems. An
important constraint is that the model be simple enough to handle small size
and unbalanced datasets, as often encountered in BCI type experiments.
Approach. The method involves linear mixed effects statistical model, wavelet
transform and spatial filtering, and aims at the characterization of localized
discriminant features in multi-sensor signals. After discrete wavelet transform
and spatial filtering, a projection onto the relevant wavelet and spatial
channels subspaces is used for dimension reduction. The projected signals are
then decomposed as the sum of a signal of interest (i.e. discriminant) and
background noise, using a very simple Gaussian linear mixed model. Main
results. Thanks to the simplicity of the model, the corresponding parameter
estimation problem is simplified. Robust estimates of class-covariance matrices
are obtained from small sample sizes and an effective Bayes plug-in classifier
is derived. The approach is applied to the detection of error potentials in
multichannel EEG data, in a very unbalanced situation (detection of rare
events). Classification results prove the relevance of the proposed approach in
such a context. Significance. The combination of linear mixed model, wavelet
transform and spatial filtering for EEG classification is, to the best of our
knowledge, an original approach, which is proven to be effective. This paper
improves on earlier results on similar problems, and the three main ingredients
all play an important role
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