Time series: theory and methods
Time series: theory and methods
Characteristics of Natural Scenes Related to the Fractal Dimension
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Science of Fractal Images
Signal processing with alpha-stable distributions and applications
Signal processing with alpha-stable distributions and applications
Robust nonlinear control design: state-space and Lyapunov techniques
Robust nonlinear control design: state-space and Lyapunov techniques
Neural Networks: A Comprehensive Foundation
Neural Networks: A Comprehensive Foundation
Chaos and Fractals
Wavelet analysis of long-range-dependent traffic
IEEE Transactions on Information Theory
Wavelet packet decompositions for the analysis of 2-D fields with stationary fractional increments
IEEE Transactions on Information Theory
Spectral representation of fractional Brownian motion in n dimensions and its properties
IEEE Transactions on Information Theory
An improved method for 2-D self-similar image synthesis
IEEE Transactions on Image Processing
Self-similar texture modeling using FARIMA processes with applications to satellite images
IEEE Transactions on Image Processing
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In the context of linear modeling, the main advantage of stable distributions is to allow the definition of non-Gaussian processes whose statistical properties are easy to characterize. In this work, we are interested in the design of a specific class of 2D discrete-space processes with stable distributions. A frequency domain method for the synthesis of these fields will be proposed which is similar to algorithms already used in the Gaussian case. The considered models represent 2D α-stable extensions of the 1D fractional Gaussian noise. They exhibit long-range dependence properties and, consequently, they could provide interesting alternatives to image modeling techniques based on the 2D fractional Brownian motion. However, the conditions for the existence of such processes deserve special attention and they are derived in this paper.