Providing a novel approach to sparsity, this comprehensive book presents the theory of
stochastic processes that are ruled by linear stochastic differential equations, and that admit …

Generalised hyperbolic (GH) processes are a class of stochastic processes that are used to
model the dynamics of a wide range of complex systems that exhibit heavy-tailed behavior …

In this paper novel simulation methods are provided for the generalised inverse Gaussian
(GIG) Lévy process. Such processes are intractable for simulation except in certain special …

Characteristic functionals are one of the main analytical tools used to quantify the statistical
properties of random fields and generalized random fields. The viewpoint taken here is that …

This work offers a necessary and sufficient condition for a stationary and ergodic process to
be lp-compressible in the sense proposed by Amini, Unser and Marvasti [“Compressibility of …

It is possible to construct Lévy white noises as generalized random processes in the sense
of Gel'fand and Vilenkin, or as an independently scattered random measures introduced by …

It is well documented that natural images are compressible in wavelet bases and tend to
exhibit fractal properties. In this paper, we investigate statistical models that mimic these …

The results of a series of theoretical studies are reported, examining the convergence rate
for different approximate representations of α-stable distributions. Although they play a key …

Although this thesis contributes to the theory of random processes, it is motivated by signal
processing applications, mainly the stochastic modeling of sparse signals. Specifically, we …

We present a statistical framework to benchmark the performance of reconstruction
algorithms for linear inverse problems, in particular, neural-network-based methods that …