Cycle-octave and related transforms in seismic signal analysis

Goupillaud, Pierre L.; Großmann, A.; Morlet, J.

doi:10.1016/0016-7142(84)90025-5

Cited by 1,269 publications

(550 citation statements)

References 4 publications

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“…The WT is a mathematical technique that has been originally introduced for timefrequency analysis of seismic data and acoustic signals [132,133,134]. In previous works [102,115], we have shown that from the space-scale WT representation of 'DNA walks', one can bring the experimental proof of the monofractal nature of DNA walk landscapes.…”

Section: Monofractality: An Essential Statistical Property Of Dna Seqmentioning

confidence: 98%

Wavelet Analysis of DNA Bending Profiles reveals Structural Constraints on the Evolution of Genomic Sequences

Audit

Vaillant

Arnéodo

et al. 2004

Journal of Biological Physics

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Abstract. Analyses of genomic DNA sequences have shown in previous works that base pairs are correlated at large distances with scale-invariant statistical properties. We show in the present study that these correlations between nucleotides (letters) result in fact from long-range correlations (LRC) between sequence-dependent DNA structural elements (words) involved in the packaging of DNA in chromatin. Using the wavelet transform technique, we perform a comparative analysis of the DNA text and of the corresponding bending profiles generated with curvature tables based on nucleosome positioning data. This exploration through the optics of the so-called 'wavelet transform microscope' reveals a characteristic scale of 100 − 200 bp that separates two regimes of different LRC. We focus here on the existence of LRC in the small-scale regime ( 200 bp). Analysis of genomes in the three kingdoms reveals that this regime is specifically associated to the presence of nucleosomes. Indeed, small scale LRC are observed in eukaryotic genomes and to a less extent in archaeal genomes, in contrast with their absence in eubacterial genomes. Similarly, this regime is observed in eukaryotic but not in bacterial viral DNA genomes. There is one exception for genomes of Poxviruses, the only animal DNA viruses that do not replicate in the cell nucleus and do not present small scale LRC. Furthermore, no small scale LRC are detected in the genomes of all examined RNA viruses, with one exception in the case of retroviruses. Altogether, these results strongly suggest that small-scale LRC are a signature of the nucleosomal structure. Finally, we discuss possible interpretations of these small-scale LRC in terms of the mechanisms that govern the positioning, the stability and the dynamics of the nucleosomes along the DNA chain. This paper is maily devoted to a pedagogical presentation of the theoretical concepts and physical methods which are well suited to perform a statistical analysis of genomic sequences. We review the results obtained with the so-called waveletbased multifractal analysis when investigating the DNA sequences of various organisms in the three kingdoms. Some of these results have been announced in B. Audit et al. [1,2].

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Section: Monofractality: An Essential Statistical Property Of Dna Seqmentioning

confidence: 98%

Wavelet Analysis of DNA Bending Profiles reveals Structural Constraints on the Evolution of Genomic Sequences

Audit

Vaillant

Arnéodo

et al. 2004

Journal of Biological Physics

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“…and as a result, the temporal localization of the wavelet becomes unsatisfactory (Goupillaud et al, 1984;Delprat et al, 1992). In the present study, we choose a wavenumber w 0 = 7, as in earlier studies (Tallon-Baudry et al, 1996;Vialatte et al, 2007); this choice yields good temporal resolution in the frequency range considered in this study.…”

Section: A1 Wavelet Transformmentioning

confidence: 99%

A comparative study of synchrony measures for the early diagnosis of Alzheimer's disease based on EEG

Dauwels

Vialatte

Musha³

et al. 2010

NeuroImage

371

384

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It is well known that EEG signals of Alzheimer's disease (AD) patients are generally less synchronous than in age-matched control subjects. However, this effect is not always easily detectable. This is especially the case for patients in the pre-symptomatic phase, commonly referred to as Mild Cognitive Impairment (MCI), during which neuronal degeneration is occurring prior to the clinical symptoms appearance. In this paper, various synchrony measures are studied in the context of AD diagnosis, including the correlation coefficient, mean-square and phase coherence, Granger causality, phase synchrony indices, information-theoretic divergence measures, state space based measures, and the recently proposed stochastic event synchrony measures. Experiments with EEG data show that many of those measures are strongly correlated (or anti-correlated) with the correlation coefficient, and hence, provide little complementary information about EEG synchrony. Measures that are only weakly correlated with the correlation coefficient include the phase synchrony indices, Granger causality measures, and stochastic-event synchrony measures. In addition, those three families of synchrony measures are mutually uncorrelated, and therefore, they each seem to capture a specific kind of interdependence. For the data set at hand, only two synchrony measures are able to convincingly distinguish AD patients from age-matched control patients, i.e., Granger causality (in particular, full-frequency directed transfer function) and stochastic event synchrony. Those two measures are used as features to distinguish MCI patients from age-matched control subjects, yielding a leave-one-out classification rate of 83%. The classification performance may be further improved by adding complementary features from EEG; this approach may eventually lead to a reliable EEG-based diagnostic tool for MCI and AD.

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“…Introduced in the early 1980s, a wavelet is a mathematical function used to divide data series into different frequency components (Goupillaud et al, 1984). The method expresses decompositions as a multitude of smaller "waves" at different frequencies (He and Guan, 2013).…”

Section: Wavelet Decompositionmentioning

confidence: 99%

Large-scale vegetation responses to terrestrial moisture storage changes

Andrew

Guan

Batelaan

2017

Hydrol. Earth Syst. Sci.

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Abstract. The normalised difference vegetation index (NDVI) is a useful tool for studying vegetation activity and ecosystem performance at a large spatial scale. In this study we use the Gravity Recovery and Climate Experiment (GRACE) total water storage (TWS) estimates to examine temporal variability of the NDVI across Australia. We aim to demonstrate a new method that reveals the moisture dependence of vegetation cover at different temporal resolutions. Time series of monthly GRACE TWS anomalies are decomposed into different temporal frequencies using a discrete wavelet transform and analysed against time series of the NDVI anomalies in a stepwise regression. The results show that combinations of different frequencies of decomposed GRACE TWS data explain NDVI temporal variations better than raw GRACE TWS alone. Generally, the NDVI appears to be more sensitive to interannual changes in water storage than shorter changes, though grassland-dominated areas are sensitive to higher-frequencies of water-storage changes. Different types of vegetation, defined by areas of land use type, show distinct differences in how they respond to the changes in water storage, which is generally consistent with our physical understanding. This unique method provides useful insight into how the NDVI is affected by changes in water storage at different temporal scales across land use types.

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Cycle-octave and related transforms in seismic signal analysis

Cited by 1,269 publications

References 4 publications

Wavelet Analysis of DNA Bending Profiles reveals Structural Constraints on the Evolution of Genomic Sequences

Wavelet Analysis of DNA Bending Profiles reveals Structural Constraints on the Evolution of Genomic Sequences

A comparative study of synchrony measures for the early diagnosis of Alzheimer's disease based on EEG

Large-scale vegetation responses to terrestrial moisture storage changes

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