M. Unser (EPFL) Tutorial: Sparse stochastic processes and biomedical image reconstruction




Date(s) : 04/02/2013   iCal
14 h 00 min - 16 h 00 min

By Michael Unser\, EPFL.\n\nTutorial: Sparse stochastic processes and biomedical image reconstruction\n\nSparse 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.\n\nThis tutorial focuses on 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 Lévy noise. We provide a complete functional characterization of these processes and highlight some of their properties.\nThe two leading threads that underly the exposition are:\n1) the statistical property of infinite divisibility\, which induces two distinct types of behavior—Gaussian vs. sparse—at the exclusion of any other\;\n2) the structural link between linear stochastic processes and spline functions which is exploited to simplify the mathematics.\n\nThe proposed continuous-domain formalism lends itself naturally to the discretization of linear inverse problems. The reconstruction is formulated as a statistical estimation problem\, which suggests some novel algorithms for biomedical image reconstruction\, including magnetic resonance imaging and X-ray tomography. We present experiments with simulated data where the proposed scheme outperforms the more traditional convex optimization techniques (in particular\, total variation).\n\nDownload slides

Catégories Pas de Catégories



Retour en haut 

Secured By miniOrange