Bootstrap for Empirical Multifractal Analysis

Wendt, Herwig; Abry, Patrice; Jaffard, Stéphane

doi:10.1109/msp.2007.4286563

Cited by 252 publications

(485 citation statements)

References 21 publications

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“…Note that the characterization provided by (27) does not require the computation of the Taylor polynomial, and that it extends to any p the previously obtained wavelet leader characterization of Hölder exponents (valid when h min > 0) [16,24]:…”

Section: P-exponent Regularity Characterization With P-leadersmentioning

confidence: 81%

“…Note the use of an L 1 normalization for the wavelet coefficients that better fits local regularity analysis and yields the correct self-similarity exponent of the wavelet coefficients for self-similar functions, see [18,16,24,32]. For further details on wavelet bases and wavelet transforms, the reader is referred to e.g., [37].…”

Section: Mother Waveletsmentioning

confidence: 99%

“…Recently, a theoretically well-grounded and practically efficient formulation that, unlike WTMM and MFDFA, extends well to higher dimensional signals, has been proposed: It relies on wavelet leaders, constructed as local suprema of discrete wavelet coefficients, cf. [16,23,24,25].…”

Section: Introductionmentioning

confidence: 99%

“…For instance, the wavelet leaders are the only multiscale quantities that were shown theoretically to be able to actually characterize the Hölder exponent [16,23,24,25]. Conversely, the practical use of a particular regularity exponent necessitates the construction of multiscale quantities specifically tailored to it, requiring the verification of global a priori regularity assumptions, which may not always hold for the data to be analyzed.…”

Section: Introductionmentioning

confidence: 99%

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p-exponent and p-leaders, Part I: Negative pointwise regularity

Jaffard

Mélot

Leonarduzzi

et al. 2016

Physica A: Statistical Mechanics and its Applications

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Multifractal analysis aims to characterize signals, functions, images or fields, via the fluctuations of their local regularity along time or space, hence capturing crucial features of their temporal/spatial dynamics. Multifractal analysis is becoming a standard tool in signal and image processing, and is nowadays widely used in numerous applications of different natures. Its common formulation relies on the measure of local regularity via the Hölder exponent, by nature restricted to positive values, and thus to locally bounded functions or signals. It is here proposed to base the quantification of local regularity on p-exponents, a novel local regularity measure potentially taking negative values. First, the theoretical properties of p-exponents are studied in detail. Second, wavelet-based multiscale quantities, the p-leaders, are constructed and shown to permit accurate practical estimation of p-exponents. Exploiting the potential dependence with p, it is also shown how the collection of p-exponents enriches the classification of locally singular behaviors in functions, signals or images. The present contribution is complemented by a companion article developing the p-leader based multifractal formalism associated to p-exponents.

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Section: P-exponent Regularity Characterization With P-leadersmentioning

confidence: 81%

Section: Mother Waveletsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

p-exponent and p-leaders, Part I: Negative pointwise regularity

Jaffard

Mélot

Leonarduzzi

et al. 2016

Physica A: Statistical Mechanics and its Applications

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“…In the present study, multifractal analysis was based on wavelet Leader, a recent method introduced in an article by Wendt et al 27 For more information, the reader is referred to the Appendix and to the reviews from Riedi and Jaffard. 14,15 Statistical Analysis Multifractal parameters are expressed as median and absolute median deviation computed over each group.…”

Section: Multifractal Analysismentioning

confidence: 99%

Multifractal Analysis of Fetal Heart Rate Variability in Fetuses with and without Severe Acidosis during Labor

et al. 2010

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We performed multifractal analysis of fetal heart rate (FHR) variability in fetuses with and without acidosis during labor. Multifractal analysis was performed on fetal electrocardiograms in 10-minute sliding windows within the last 2 hours before delivery in 45 term fetuses divided in three groups according to umbilical arterial pH and FHR pattern: group A had pH !7.30 and normal FHR, group B had pH !7.30 and intermediate or abnormal FHR, and group C had acidosis (pH 7.05) and intermediate or abnormal FHR. Six multifractal parameters were compared using Wilcoxon rank sum test. Multifractal parameters were significantly different between the three groups in the last 10 minutes before delivery (p <0.05). Two parameters (h min , zeta(2)) exhibited a significant difference 70 minutes before delivery, and one parameter (C 2 ) was different 10 minutes before birth (p <0.05). Multifractal parameters were significantly different in acidotic and nonacidotic fetuses, independently from FHR pattern.

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Wavelet Methods for Multifractal Analysis of Functions

Jaffard¹

2009

Scaling, Fractals and Wavelets

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Bootstrap for Empirical Multifractal Analysis

Cited by 252 publications

References 21 publications

p-exponent and p-leaders, Part I: Negative pointwise regularity

p-exponent and p-leaders, Part I: Negative pointwise regularity

Multifractal Analysis of Fetal Heart Rate Variability in Fetuses with and without Severe Acidosis during Labor

Wavelet Methods for Multifractal Analysis of Functions

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