Wavelet Leaders in Multifractal Analysis

Jaffard, Stéphane; Lashermes, Bruno; Abry, Patrice

doi:10.1007/978-3-7643-7778-6_17

Cited by 132 publications

(179 citation statements)

References 52 publications

Supporting

Mentioning

173

Contrasting

Unclassified

Order By: Relevance

“…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%

See 1 more Smart Citation

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

Jaffard

Mélot

Leonarduzzi

et al. 2016

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Jaffard

Mélot

Leonarduzzi

et al. 2016

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

show abstract

“…However, GMWP and DFA loc both had a larger overestimation of the spectrum width of monofractal signals, as compared with MFDFA, LWT, and entropy analysis. A shortcoming of the benchmark test conducted by Turiel et al (2008) was the inclusion of other multifractal analyses based on q-order statistics, which have inferior performance, as compared with analyses included in the present study (Jaffard, Lashermes, & Abry, 2006;Oświęcimka, Kwapien, & Drozdz, 2006;Serrano & Figliola, 2009). Another shortcoming of the benchmark test conducted by Turiel et al (2008) was the use of random cascades that are not appropriate candidates to mimic the intermittent variation in behavioral variables by their scale-discrete nature and strictly positive values.…”

Section: Discussionmentioning

confidence: 95%

Multifractal analyses of response time series: A comparative study

Ihlen

2013

Behav Res

View full text Add to dashboard Cite

Response time series with a non-Gaussian distribution and long-range dependent dynamics have been reported for several cognitive tasks. Conventional monofractal analyses numerically define a long-range dependency as a single scaling exponent, but they assume that the response times are Gaussian distributed. Ihlen and Vereijken (Journal of Experimental Psychology: General, 139, 436-463, 2010) suggested multifractal extensions of the conventional monofractal analyses that are more suitable when the response time has a non-Gaussian distribution. Multifractal analyses estimate a multifractal spectrum of scaling exponents that contain the single exponent estimated by the conventional monofractal analyses. However, a comparison of the performance of multifractal analyses with behavioral variables has not yet been addressed. The present study compares the performance of seven multifractal analyses. The multifractal analyses were tested on multiplicative cascading noise that generates time series with a predefined multifractal spectrum and with a structure of variation that mimics intermittent response time variation. Time series with 1,024 and 4,096 samples were generated with additive noise and multiharmonic trends of two different magnitudes (signal-to-noise/trend ratio; 0.33 and 1). The results indicate that all multifractal analysis has individual pros and cons related to sample size, multifractality, and the presence of additive noise and trends in the response time series. The summary of pros and cons of the seven multifractal analyses provides a guideline for the choice of multifractal analyses of response time series and other behavioral variables.

show abstract

“…Do ponto de vista prático, o termo ( √ a) −1 apresentado na Equação 3é substituído por (a) −1 . Mais detalhes podem ser encontrados em [29,34]. Um exemplo de uso da CWT com essa normalização L 1é encontrado no pacote FRACLAB, do ambiente scilab 3 , queé indicado para estudos de sinais fractais, ou em [28], em que estudos da amplitude do sinal são de interesse.…”

Section: Normalizaçõesunclassified

Explorando a transformada wavelet contínua

Domingues

Mendes

Kaibara

et al. 2016

Rev. Bras. Ensino Fís.

View full text Add to dashboard Cite

A transformada wavelet contínua constitui poderosa ferramenta para análise multiescala de dados. Ela tem amplas aplicações na Física, na Matemática, nas Ciências Naturais e, inclusive, grande apelo nas engenharias, computação eáreas de tecnologia e inovação. Do ponto de vista introdutório, a transformada wavelet tem sido abordada amplamente em trabalhos anteriores. Assim, esta apresentação dáênfase ao uso dessa técnica em situações teóricas e práticas que normalmente não são exploradas; porém fundamentais para um uso mais adequado, ou mesmo correto, dessa ferramenta. Um embasamento consistente possibilita, sobretudo, uma extensão de sua aplicação para novas pesquisas, facilitadas pela disponibilidade de programas e ferramentas gratuitas e, até, várias dessas sob a forma de recursos de livre distribuição (free softwares). Por critério de escolha dos autores, apresentam-se, neste artigo, conceitos e exemplos de técnicas que podem ser de grande interesse para vários tipos de estudos na Física e em outrasáreas correlatas. Este texto destina-se a pesquisadores, professores e estudantes de pós-graduação, com a possibilidade de atender ainda necessidades de estudantes dosúltimos anos de graduação. Palavras-chave: wavelet, sinais multiescala, análise de sinais.The continuous wavelet transform is a powerful tool for multiscale data analysis. It has wide applications in physics, mathematics, natural sciences and even great appeal in engineering, computing and areas of technology and innovation. As an introductory point of view, the wavelet transform has been widely addressed in previous works. Thus, this presentation emphasizes the use of this technique in theoretical and practical situations that are not usually explored, but situations that are fundamental to a better use, or even a correct use, of this tool. Consistent bases enable mainly extensions of wavelet application to new investigations, that are facilitated by the availability of free programs and tools, and even several of these in completely available distribution of resources (free softwares). The content of this article, by the authors' choice criteria, presents concepts and examples of techniques that can be of great interest for various studies in physics and other related areas. This text is aimed at researchers, teachers and graduate students, with the possibility of still meet the preparation needs of students at last undergraduation stage. Keywords: wavelet, multiscale signals, signal analysis. IntroduçãoA teoria wavelet causou um frenesi na comunidade científica nasúltimas décadas e gerou um fenômeno de interesse, na pesquisa e na aplicação, com crescimento exponencial, gerando dezenas de milhares * Endereço de correspondência: margarete.domingues@inpe.br.de publicações, patentes e prêmios internacionais associados [8]. O leitor e sua família já participam e conhecem os efeitos desse fenômeno, tanto ao utilizar as imagens jpeg de um celular que podem ser enviadas por internet, quanto ao assistir os filmes de animação 3D, ou mesmo a ter seus dados bio...

show abstract

Wavelet Leaders in Multifractal Analysis

Cited by 132 publications

References 52 publications

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

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

Multifractal analyses of response time series: A comparative study

Explorando a transformada wavelet contínua

Contact Info

Product

Resources

About