Synthesis of bidimensional α-stable models with long-range dependence

Abstract

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.