2D Anisotropic Wavelet Entropy with an Application to Earthquakes in Chile

Nicolis, Orietta; Mateu, Jorge

doi:10.3390/e17064155

Cited by 17 publications

(11 citation statements)

References 60 publications

(59 reference statements)

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“…Furthermore, these results could easily be extended to the n− dimensional case. Some generalizations could also be considered for the study of anisotropic fractional Brownian fields by taking into account continuous wavelet transform, such as fully anisotropic wavelets introduced by [44] and successively used by [28]. Finally, our future steps are evaluating and validating these results on real datasets.…”

Section: Discussionmentioning

confidence: 99%

“…A definition of Shannon wavelet entropy based on the energy distribution of wavelet coefficients was proposed by [21][22][23][24][25][26][27]. In particular, Sello [21] defined temporal wavelet entropy using continuous wavelets, and [20] introduced multiresolution wavelet entropy by summing the energy for all discrete times, and discretizing scale j. Nicolis and Mateu [28] used the anisotropic Morlet wavelet to define Shannon entropy in two-dimensional point processes. A discrete version of Shannon wavelet entropy was proposed by [25][26][27][29][30][31][32] to characterize self-similar processes with Gaussian and stationary increments.…”

Section: Introductionmentioning

confidence: 99%

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Wavelet-Based Entropy Measures to Characterize Two-Dimensional Fractional Brownian Fields

Nicolis

Mateu

Contreras-Reyes

2020

Entropy

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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.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Wavelet-Based Entropy Measures to Characterize Two-Dimensional Fractional Brownian Fields

Nicolis

Mateu

Contreras-Reyes

2020

Entropy

Self Cite

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“…In [ 14 ], the authors served of Daubechies wavelets to construct an entropy measure for biomedical images efficiency proof. See also [ 15 , 16 , 17 , 18 ].…”

Section: Introduction and Motivationmentioning

confidence: 99%

Clifford Wavelet Entropy for Fetal ECG Extraction

Jallouli

Arfaoui

Mabrouk

et al. 2021

Entropy

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Analysis of the fetal heart rate during pregnancy is essential for monitoring the proper development of the fetus. Current fetal heart monitoring techniques lack the accuracy in fetal heart rate monitoring and features acquisition, resulting in diagnostic medical issues. The challenge lies in the extraction of the fetal ECG from the mother ECG during pregnancy. This approach has the advantage of being a reliable and non-invasive technique. In the present paper, a wavelet/multiwavelet method is proposed to perfectly extract the fetal ECG parameters from the abdominal mother ECG. In a first step, due to the wavelet/mutiwavelet processing, a denoising procedure is applied to separate the noised parts from the denoised ones. The denoised signal is assumed to be a mixture of both the MECG and the FECG. One of the well-known measures of accuracy in information processing is the concept of entropy. In the present work, a wavelet/multiwavelet Shannon-type entropy is constructed and applied to evaluate the order/disorder of the extracted FECG signal. The experimental results apply to a recent class of Clifford wavelets constructed in Arfaoui, et al. J. Math. Imaging Vis. 2020, 62, 73–97, and Arfaoui, et al.Acta Appl. Math.2020, 170, 1–35.. Additionally, classical Haar–Faber–Schauder wavelets are applied for the purpose of comparison. Two main well-known databases have been applied, the DAISY database and the CinC Challenge 2013 database. The achieved accuracy over the test databases resulted in Se=100%, PPV=100% for FECG extraction and peak detection.

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“…Telesca et al (Telesca et al, 2014) applied the Fisher-Shannon method to confirm the correlation between the properties of the geoelectrical signals and crust deformation in three sites in Taiwan. Nicolis et al (Nicolis et al, 2015) adopted a combined Shannon entropy and wavelet-based approach to measure the spatial heterogeneity and complexity of spatial point patterns for a catalogue of earthquake events in Chile.…”

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confidence: 99%

Measuring the seismic risk along the Nazca-Southamerican subduction front: Shannon entropy and mutability

Vogel¹,

Brevis²,

Pastén³

et al. 2020

Preprint

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Abstract. Four geographical zones are deﬁned along the trench that is formed due to the subduction of the Nazca Plate underneath the South American plate; they are denoted A, B, C and D from North to South; zones A, B, and D had a major earthquake after 2010 (Magnitude over 8.0), while zone C has not, thus oﬀering a contrast for comparison. For each zone a sequence of intervals between consecutive seisms with magnitudes ≥ 3.0 is set up and then characterized by Shannon entropy and mutability. These methods show correlation after a major earthquake in what is known as the aftershock regime, but show independence otherwise. Exponential adjustments for these parameters reveal that mutability oﬀers a wider range for the parameters characterizing the recovery compared to the values of the parameters deﬁning the background activity for each zone before a large earthquake. It is found that the background activity is particularly high for zone A, still recovering for zone B, reaching values similar to those of zone A in the case of zone C (without recent major earthquake) and oscillating around moderate values for zone D. It is discussed how this can be an indication for more risk for an important future seism in the cases of zones A and C. The similarities and diﬀerences between Shannon entropy and mutability are discussed and explained.

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2D Anisotropic Wavelet Entropy with an Application to Earthquakes in Chile

Cited by 17 publications

References 60 publications

Wavelet-Based Entropy Measures to Characterize Two-Dimensional Fractional Brownian Fields

Wavelet-Based Entropy Measures to Characterize Two-Dimensional Fractional Brownian Fields

Clifford Wavelet Entropy for Fetal ECG Extraction

Measuring the seismic risk along the Nazca-Southamerican subduction front: Shannon entropy and mutability

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