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Wavelet-Based Entropy Measures to Characterize Two-Dimensional Fractional Brownian Fields.
Orietta Nicolis1, Jorge Mateu2, Javier E Contreras-Reyes3
1Facultad de Ingenieria, Universidad Andres Bello, Viña del Mar 2520000, Chile.
Entropy (Basel, Switzerland)
|December 8, 2020
Summary
This study extends fractional Brownian field analysis to two dimensions using wavelet entropy methods. The research successfully characterizes 2D self-similar processes, advancing fractal analysis techniques.
Area of Science:
- Physics
- Information Theory
- Data Analysis
Background:
- Previous work by Perez et al. established methods for analyzing fractional Brownian fields.
- Characterizing complex, self-similar processes requires robust analytical tools.
- Two-dimensional (2D) analysis presents unique challenges compared to 1D studies.
Purpose of the Study:
- To extend the analysis of fractional Brownian fields to two dimensions (2D).
- To define and apply Shannon, Tsallis, and Rényi entropies in a 2D context.
- To estimate the Hurst exponent using wavelet spectrum regression in 2D.
Main Methods:
- Definition of Shannon entropy based on the 2D wavelet spectrum.
- Estimation of the Hurst exponent via regression of log square coefficients against resolution levels.
- Application of Tsallis and Rényi entropy definitions in the 2D fractional Brownian field.
Main Results:
- Successful extension of entropy-based analysis to the 2D fractional Brownian field.
- Demonstration of the methodology's ability to characterize 2D self-similar processes (α = 2).
- Validation of the Hurst exponent estimation through wavelet spectrum analysis.
Conclusions:
- The developed wavelet entropy methodology is effective for characterizing 2D self-similar processes.
- This approach provides a robust framework for analyzing complex 2D fractal data.
- The study advances the understanding and analytical capabilities for 2D fractional Brownian fields.
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