scholarly journals The hyperbolic wavelet transform: an efficient tool for multifractal analysis of anisotropic fields

2015 ◽  
Vol 31 (1) ◽  
pp. 313-348 ◽  
Author(s):  
Patrice Abry ◽  
Marianne Clausel ◽  
Stéphane Jaffard ◽  
Stéphane Roux ◽  
Béatrice Vedel
Keyword(s):  
Wavelet Transform ◽  
Multifractal Analysis ◽  
Efficient Tool ◽  
Anisotropic Fields

ENTROPIC AND MULTIFRACTAL ANALYSIS OF DISORDERED MORPHOLOGIES

Fractals ◽  
1993 ◽  
Vol 01 (03) ◽  
pp. 671-679 ◽  
Author(s):  
A. BEGHDADI ◽  
C. ANDRAUD ◽  
J. LAFAIT ◽  
J. PEIRO ◽  
M. PERREAU
Keyword(s):  
Multifractal Analysis ◽  
Characteristic Length ◽  
Finite Size ◽  
Morphological Parameter ◽  
Efficient Tool ◽  
Optimum Length ◽  
Maximum Information ◽  
Configuration Entropy ◽  
Simulated Images

We propose the configuration entropy as an efficient tool of characterization of the disorder of random morphologies and as a pertinent morphological parameter for describing the optical properties. When increasing the size of observation of an image, it undergoes a maximum at a characteristic length which is the optimum length at which the image must be observed to get the maximum information. When applied to computer simulated images, the configuration entropy is more powerful, less ambiguous and less sensitive to the finite size of images than the generalized fractal dimension.

DETECTION OF ATMOSPHERIC TURBULENCE BY MULTIFRACTAL ANALYSIS USING WAVELETS

Fractals ◽  
2004 ◽  
Vol 12 (02) ◽  
pp. 211-221 ◽  
Author(s):  
M. NICOLLET ◽  
A. LEMARCHAND ◽  
N. CAVACIUTI
Keyword(s):  
Wavelet Transform ◽  
Atmospheric Turbulence ◽  
Multifractal Analysis ◽  
Function Method ◽  
Lower Stratosphere ◽  
Thin Layers ◽  
Scaling Exponents ◽  
Wavelet Transform Modulus Maxima ◽  
Modulus Maxima ◽  
Balloon Measurements

We study the singularities of a temperature profile obtained by means of balloon measurements in the troposphere and lower stratosphere. The data give the evolution of the temperature as the altitude of the probe increases. We compare the scaling exponents deduced from the Wavelet Transform Modulus Maxima (WTMM) method and the structure function method. In the lower stratosphere, the variations in the multifractal properties with the altitude deduced from wavelets allow us to detect thin layers of about 200 m depth exhibiting atmospheric turbulence.

scholarly journals WAVELET-BASED MULTIFRACTAL FORMALISM TO ASSIST IN DIAGNOSIS IN DIGITIZED MAMMOGRAMS

2011 ◽  
Vol 20 (3) ◽  
pp. 169 ◽  
Author(s):  
Pierre Kestener ◽  
Jean Marc Lina ◽  
Philippe Saint-Jean ◽  
Alain Arneodo
Keyword(s):  
Wavelet Transform ◽  
Hurst Exponent ◽  
Multifractal Analysis ◽  
Computer Assisted ◽  
Scaling Properties ◽  
Multifractal Formalism ◽  
Long Range Correlations ◽  
Multifractal Scaling ◽  
Self Similar ◽  
Assisted Diagnosis

We apply the 2D wavelet transform (WTMM) method to perform a multifractal analysis of digitized mammograms. We show that normal regions display monofractal scaling properties as characterized by the socalled Hurst exponent H =0.3±0.1 in fatty areas which look like antipersistent self-similar random surfaces, while H=0.65±0.1 in dense areas which exibit long-range correlations and possibly multifractal scaling properties. We further demonstrate that the 2D WTMM method provides a very efficient way to detect tumors as well as microcalcifications (MC) which correspond to much stronger singularities than those involved in the background tissue roughness fluctuations. These preliminary results indicate that the texture discriminatory power of the 2D WTMM method may lead to significant improvement in computer-assisted diagnosis in digitized mammograms.

scholarly journals Multifractal Analysis of SARS-CoV-2 Coronavirus genomes using the wavelet transform

2020 ◽  
Author(s):  
Sid-Ali Ouadfeul
Keyword(s):  
Wavelet Transform ◽  
Hurst Exponent ◽  
Multifractal Analysis ◽  
Genome Structure ◽  
The Self ◽  
Self Organization ◽  
Dna Coding ◽  
Wavelet Transform Modulus Maxima ◽  
Range Correlation ◽  
Modulus Maxima

AbstractIn this paper, the 1D Wavelet Transform Modulus Maxima lines (WTMM) method is used to investigate the Long-Range Correlation (LRC) and to estimate the so-called Hurst exponent of 21 isolate RNA sequence downloaded from the NCBI database of patients infected by SARS-CoV-2, Coronavirus, the Knucleotidic, Purine, Pyramidine, Ameno, Keto and GC DNA coding are used. Obtained results show the LRC character in the most sequences; except some sequences where the anti-correlated or the Classical Brownian motion character is observed, demonstrating that the SARS-Cov2 coronavirus undergoes mutation from a country to another or in the same country, they reveals also the complexity and the heterogeneous genome structure organization far from the equilibrium and the self-organization.

LOCAL SCALING PROPERTIES OF FRACTALS OBSERVED IN Ni-Zr ALLOY FILMS

1990 ◽  
Vol 04 (17) ◽  
pp. 1111-1118 ◽  
Author(s):  
J.R. DING ◽  
F. WANG ◽  
B.X. LIU
Keyword(s):  
Wavelet Transform ◽  
Mass Distribution ◽  
Multifractal Analysis ◽  
Ion Irradiation ◽  
Potential Gradient ◽  
Alloy Films ◽  
Scaling Properties ◽  
Local Scaling ◽  
Wide Range ◽  
Zr Alloy

Wavelet transform was performed based on the fractals observed in Ni-Zr alloy films during ion irradiation. The mass distribution measure and the Laplacian potential gradient measure were used to study the local scaling properties of the ion-induced fractals. The strength of singularities at each point was calculated according to the wavelet transform. The densities of the strength of singularities were also deduced and compared with the f-α spectra yielded by multifractal analysis. The results showed that the ion-induced fractals had a wide range of strength of singularities.

scholarly journals Multifractal Analysis of Signals Based on Wavelet-Transform

2007 ◽  
Vol 7 (1) ◽  
pp. 3-25 ◽  
Author(s):  
Alexyi Nikolaevich Pavlov ◽  
◽  
Vadim Semenovich Anishchenko ◽  
Keyword(s):  
Wavelet Transform ◽  
Multifractal Analysis

scholarly journals DETERMINING LOCAL SINGULARITY STRENGTHS AND THEIR SPECTRA WITH THE WAVELET TRANSFORM

Fractals ◽  
2000 ◽  
Vol 08 (02) ◽  
pp. 163-179 ◽  
Author(s):  
ZBIGNIEW R. STRUZIK
Keyword(s):  
Wavelet Transform ◽  
Multifractal Analysis ◽  
Real Life ◽  
Life Time ◽  
Hölder Exponent ◽  
Multifractal Formalism ◽  
Wavelet Transform Modulus Maxima ◽  
Local Singularity ◽  
Modulus Maxima ◽  
Multiplicative Cascade

We present a robust method of estimating the effective strength of singularities (the effective Hölder exponent) locally at an arbitrary resolution. The method is motivated by the multiplicative cascade paradigm, and implemented on the hierarchy of singularities revealed with the wavelet transform modulus maxima (WTMM) tree. In addition, we illustrate the direct estimation of the scaling spectrum of the effective singularity strength, and we link it to the established partition function-based multifractal formalism. We motivate both the local and the global multifractal analysis by showing examples of computer-generated and real-life time series.

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