Publications associées à Gaussian versus Sparse Stochastic Processes

A Unified Formulation of Gaussian Versus Sparse Stochastic Processes-Part I: Continuous-Domain Theory

We introduce a general distributional framework that results in a unifying description and characterization of a rich variety of continuous-time stochastic processes. The cornerstone of our approach is an innovation model that is driven by some generalized ...

Ieee-Inst Electrical Electronics Engineers Inc2014

A Unified Formulation of Gaussian Versus Sparse Stochastic Processes-Part II: Discrete-Domain Theory

Michaël Unser, Arash Amini, Pouya Dehghani Tafti, Hagay Kirshner

This paper is devoted to the characterization of an extended family of continuous-time autoregressive moving average (CARMA) processes that are solutions of stochastic differential equations driven by white Levy innovations. These are completely specified ...

Ieee-Inst Electrical Electronics Engineers Inc2014

On the Continuity of Characteristic Functionals and Sparse Stochastic Modeling

Michaël Unser, Julien René Pierre Fageot, Arash Amini

The characteristic functional is the infinite-dimensional generalization of the Fourier transform for measures on function spaces. It characterizes the statistical law of the associated stochastic process in the same way as a characteristic function specif ...

Springer Birkhauser2014

Compressed Sensing of Memoryless Sources

Saeid Haghighatshoar

Compressed sensing is a new trend in signal processing for efficient sampling and signal acquisition. The idea is that most real-world signals have a sparse representation in an appropriate basis and this can be exploited to capture the sparse signal by ta ...

EPFL2014

Invariant manifolds with boundary for jump-diffusions

Damir Filipovic

We provide necessary and sufficient conditions for stochastic invariance of finite dimensional submanifolds with boundary in Hilbert spaces for stochastic partial differential equations driven by Wiener processes and Poisson random measures. ...

Univ Washington, Dept Mathematics2014

Statistics of Wavelet Coefficients for Sparse Self-Similar Images

Michaël Unser, Julien René Pierre Fageot, Emrah Bostan

We study the statistics of wavelet coefficients of non-Gaussian images, focusing mainly on the behaviour at coarse scales. We assume that an image can be whitened by a fractional Laplacian operator, which is consistent with an

∥ω∥ ^{ -\gamma }

spectral ...

IEEE2014

Discrete stochastic heat equation driven by fractional noise

Kamran Kalbasi

We consider the parabolic Anderson model on

\mathbb{Z}^d

driven by fractional noise. We prove that it has a mild solution given by Feynman-Kac representation which coincides with the partition function of a directed polymer in a fractional Brownian envir ...

EPFL2014

STOCHASTIC PROCESSES AND CONSTRUCTION OF BROWNIAN MOTION

Christophe-Aschkan Mery

This project offers a rigorous introduction to the tools needed to construct a continuous stochastic process. Among other things, we give a very detailed proof of the Kolmogorov continuity criterion. We then construct a Brownian Motion following the formal ...

EPFL2013

Stochastic Control and Free Boundary Problems for Sailboat Trajectory Optimization

Laura Vinckenbosch

The topic of this thesis is the study of several stochastic control problems motivated by sailing races. The goal is to minimize the travel time between two locations, by selecting the fastest route in face of randomly changing weather conditions, such as ...

EPFL2012

The Analog Formulation of Sparsity Implies Infinite Divisibility and Rules Out Bernoulli-Gaussian Priors

Michaël Unser, Arash Amini, Ulugbek Kamilov

Motivated by the analog nature of real-world signals, we investigate continuous-time random processes. For this purpose, we consider the stochastic processes that can be whitened by linear transformations and we show that the distribution of their samples ...

Ieee2012

Gaussian versus Sparse Stochastic Processes

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A Unified Formulation of Gaussian Versus Sparse Stochastic Processes-Part I: Continuous-Domain Theory

A Unified Formulation of Gaussian Versus Sparse Stochastic Processes-Part II: Discrete-Domain Theory

On the Continuity of Characteristic Functionals and Sparse Stochastic Modeling

Compressed Sensing of Memoryless Sources

Invariant manifolds with boundary for jump-diffusions

Statistics of Wavelet Coefficients for Sparse Self-Similar Images

Discrete stochastic heat equation driven by fractional noise

STOCHASTIC PROCESSES AND CONSTRUCTION OF BROWNIAN MOTION

Stochastic Control and Free Boundary Problems for Sailboat Trajectory Optimization

The Analog Formulation of Sparsity Implies Infinite Divisibility and Rules Out Bernoulli-Gaussian Priors

A Unified Formulation of Gaussian Versus Sparse Stochastic Processes-Part I: Continuous-Domain Theory

Invariant manifolds with boundary for jump-diffusions

A Unified Formulation of Gaussian Versus Sparse Stochastic Processes-Part II: Discrete-Domain Theory

The Analog Formulation of Sparsity Implies Infinite Divisibility and Rules Out Bernoulli-Gaussian Priors

On the Continuity of Characteristic Functionals and Sparse Stochastic Modeling

Discrete stochastic heat equation driven by fractional noise

Compressed Sensing of Memoryless Sources

Statistics of Wavelet Coefficients for Sparse Self-Similar Images

STOCHASTIC PROCESSES AND CONSTRUCTION OF BROWNIAN MOTION

Stochastic Control and Free Boundary Problems for Sailboat Trajectory Optimization