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UID:5491@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20130204T140000
DTEND;TZID=Europe/Paris:20130204T160000
DTSTAMP:20241028T215850Z
URL:https://www.i2m.univ-amu.fr/evenements/m-unser-epfl-tutorial-sparse-st
 ochastic-processes-and-biomedical-image-reconstruction/
SUMMARY: (...): M. Unser (EPFL)  Tutorial: Sparse stochastic processes and 
 biomedical image reconstruction
DESCRIPTION:: By Michael Unser\\\, EPFL.\n\nTutorial: Sparse stochastic pro
 cesses and biomedical image reconstruction\n\nSparse stochastic processes 
 are continuous-domain processes that admit a parsimonious representation i
 n some matched wavelet-like basis. Such models are relevant for image comp
 ression\\\, compressed sensing\\\, and\\\, more generally\\\, for the deri
 vation 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\\\, equivalentl
 y\\\, as solutions of linear stochastic differential equations driven by w
 hite Lévy noise. We provide a complete functional characterization of the
 se processes and highlight some of their properties.\nThe two leading thre
 ads that underly the exposition are:\n1) the statistical property of infin
 ite divisibility\\\, which induces two distinct types of behavior—Gaussi
 an vs. sparse—at the exclusion of any other\\\;\n2) the structural link 
 between linear stochastic processes and spline functions which is exploite
 d 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\\\, w
 hich suggests some novel algorithms for biomedical image reconstruction\\\
 , including magnetic resonance imaging and X-ray tomography. We present ex
 periments with simulated data where the proposed scheme outperforms the mo
 re traditional convex optimization techniques (in particular\\\, total var
 iation).\n\nDownload slides
CATEGORIES:Séminaire,Signal et Apprentissage
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