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

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

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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

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