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Análisis multifractal basado en coeficientes ondita líderes: formalismo multifractal basado en p-líderes y aplicación a señales biomédicas

Roberto Fabio Leonarduzzi María Eugenia Torres Hugo Aimar Juan Carlos Gómez Carlos Muravchik Patrice Abry

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Resumen/Descripción – provisto por el repositorio digital
Multifractal analysis and scale invariance constitute relevant and popular paradigms for the analysis, modelling and characterization of irregular signals. Essentially, their use amounts to the identification of the power-law decay of some adequate multiresolution quantity. Its application requires the careful selection of the scaling range where those power-laws are observed. This selection is performed by visual inspection without theoretical guidelines. Also, multiresolution quantities in current use, which are based on the Hölder exponent, can not be used on signals that are characterized by negative regularity. The accepted solution to this limitation is a preprocessing step which can lead to erroneous estimations in presence of oscillating singularities. The first contribution of this thesis is an algorithm for the selection of the scaling range in a non-parametric, automated and unsupervised way. We validate the method by means of numerical simulations. We show that the algorithm selects correct ranges, and we illustrate how it adapts to departures of scaling. The second contribution is the proposition and development of a multifractal formalism, based on wavelet p-leaders, that intrinsically allows to analyze data with negative regularity. We illustrate its performance by means of numerical simulations. We discuss the information provided by changing the parameter p. We establish an explicit relationship with multifractal detrended fluctuation analysis (MFDFA). Finally, we illustrate its application to acidosis detection from fetal heart rate.
Palabras clave – provistas por el repositorio digital

Multifractal analysis; Scale invariance; Scaling range; Bootstrap; p-leaders; p-exponent; Análisis multifractal; Invarianza a la escala; Rango de escalamiento; p-líderes; p-exponente

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No requiere 2014 Biblioteca Virtual de la Universidad Nacional del Litoral (SNRD) acceso abierto

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Tipo de recurso:

tesis

Idiomas de la publicación

  • español castellano

País de edición

Argentina

Fecha de publicación