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SUMMARY:Generalized stochastic processes as prior models for compressed se
 nsing and sparse signal recovery
DTSTART:20120330T101500
DTEND:20120330T111500
DTSTAMP:20260408T085049Z
UID:399049f64c2637870b09ae683ef517f8b2f88c94d4adfc6c77ba1731
CATEGORIES:Conferences - Seminars
DESCRIPTION:Michael Unser\nWe present a general\, non-Gaussian statistical
  framework for the reconstruction of signals from a limited set of noisy l
 inear measurements and compressed sensing. The underlying signals are cont
 inuously-defined and modeled as sparse stochastic processes (SSP).\nPart I
 : Theory. SSP are generalized stochastic processes (in the sense Gelfand a
 nd Vilenkin) that are solutions of (potentially unstable) linear stochasti
 c differential equations. They are described by a general innovation model
  that is specified by: 1) a whitening operator L\, which shapes their Four
 ier spectrum\, and 2) a Lévy exponent f\, which controls the sparsity of 
 the (non-Gaussian) innovations (white Lévy noise). We give sufficient con
 ditions on (L\,f) for these processes to be welldefined and derive their c
 haracteristic form which provides a complete statistical description. We a
 lso substantiate the claim that the observations of these processes are in
 trinsically sparse (with heavy tailed statistics).\nPart II: Application. 
 Using those results\, we derive an extended family of MAP estimators that 
 are directly applicable to biomedical image reconstruction. While our fami
 ly of estimators includes the traditional methods of Tikhonov and total-va
 riation (TV) regularization as particular cases\, it opens the door to a m
 uch broader class of potential functions (associated with infinitely divis
 ible priors) that are inherently sparse and typically nonconvex. By introd
 ucing a discrete counterpart of the\ninnovation variables\, we are able to
  develop an alternating minimization scheme that can handle arbitrary pote
 ntial functions. We apply our framework to the reconstruction of magnetic 
 resonance images and phase-contrast tomograms\; we also present simulation
  examples where the proposed scheme outperforms the more traditional conve
 x optimization techniques (in particular\, TV).
LOCATION:AAC006 http://plan.epfl.ch/?zoom=20&recenter_y=5864224.20313&rece
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STATUS:CONFIRMED
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