Abstract
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, ) self-similar processes.
Highlights
The concept of entropy was first introduced by [1] in thermodynamics as a measure of the amount of energy in a system
Entropy is a measure of uncertainty and unpredictability associated with a random variable, and Shannon entropy quantifies the expected value of information generated from a random variable
We extend the definition of wavelet Shannon entropy proposed by [25,26,27] to provide a characterization of an isotropic n-dimensional fractional Brownian field
Summary
The concept of entropy was first introduced by [1] in thermodynamics as a measure of the amount of energy in a system. A definition of Shannon wavelet entropy based on the energy distribution of wavelet coefficients was proposed by [21,22,23,24,25,26,27]. A similar approach based on wavelet probability densities was proposed by [33] using the Fisher–Shannon method [15] The latter authors used a definition of wavelet entropy for characterizing self-similar processes in the time domain, but an extension to the two-dimensional case has not been proposed so far. We extend the definition of wavelet Shannon entropy proposed by [25,26,27] to provide a characterization of an isotropic n-dimensional fractional Brownian field.
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