BIOMEDICAL IMAGING GROUP (BIG)
Laboratoire d'imagerie biomédicale (LIB)

Sparse Stochastic Processes: A Continuous-Domain Statistical Framework for Compressed Sensing

M. Unser

Plenary talk, Signal Processing with Adaptive Sparse Structured Representations (SPARS'13), Lausanne VD, Swiss Confederation, July 8-11, 2013.

We introduce an extended family of sparse processes that are specified by a generic (non-Gaussian) innovation model or, equivalently, as solutions of linear stochastic differential equations driven by white Levy noise. We present the mathematical tools for their characterization. The two leading threads of the exposition are: the statistical property of infinite divisibility, which induces two distinct types of behavior—Gaussian vs. sparse—at the exclusion of any other; the structural link between linear stochastic processes and splines. This allows us to prove that these processes admit a parsimonious representation in some matched wavelet-like basis. We show that these models have predictive power for image compression and that they are applicable to the derivation of statistical algorithms for solving ill-posed inverse problems, including compressed sensing. 

@INPROCEEDINGS(http://bigwww.epfl.ch/publications/unser1303.html,
AUTHOR="Unser, M.",
TITLE="Sparse Stochastic Processes: {A} Continuous-Domain Statistical
	Framework for Compressed Sensing",
BOOKTITLE="Signal Processing with Adaptive Sparse Structured
	Representations ({SPARS'13})",
YEAR="2013",
editor="",
volume="",
series="",
pages="",
address="Lausanne VD, Swiss Confederation",
month="July 8-11,",
organization="",
publisher="",
note="Plenary talk")
© 2013 FNSNF. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from FNSNF. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.