Sparse stochastic processes with applications to signal processing

Datum

18.10.2017

Zeit

17:00 - 18:00

Sprecher

Prof. Michael Unser

Zugehörigkeit

École Polytechnique Fédérale de Lausanne, Switzerland

Serie

TUD Dresdner Mathematisches Seminar

Sprache

en

Hauptthema

Mathematik

Andere Themen

Mathematik

Host

Pof. Dr. Rene Schilling

Beschreibung

Sparse stochastic processes are continuous-domain processes that admit a parsimonious representation in some matched wavelet-like basis. Such models are relevant for image compression, compressed sensing, and, more generally, for the derivation of statistical algorithms for solving ill-posed inverse problems. In this presentation, we first show how such processes can be specified by a generic (non-Gaussian) innovation model or, equivalently, as solutions of linear stochastic differential equations driven by white Lévy noise. We present a distributional formalism that provides a complete characterization, including the description of their transform-domain statistics. We then apply these models to the derivation of signal-processing algorithms. In particular, we obtain MAP estimators that are compatible with popular sparsity-promoting processing schemes—such as total-variation regularization and l1-norm minimization. Examples of applications include audio coding, denoising, and the reconstruction of biomedical images from noisy and/or incomplete data.

Letztmalig verändert: 04.10.2017, 11:01:22