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SUMMARY:On Convex Finite-Dimensional Variational Methods in Imaging Scienc
 es\, and Hamilton-Jacobi Equations - Darbon\, J (University of California\
 , Los Angeles)
DTSTART:20140212T110000Z
DTEND:20140212T114500Z
UID:TALK50822@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We consider standard finite-dimensional variational models use
 d in signal/image processing that consist in minimizing an energy involvin
 g a data fidelity term and a regularization term. We propose new remarks f
 rom a theoretical perspective which give a precise description on how the 
 solutions of the optimization problem depend on the amount of smoothing ef
 fects and the data itself. The dependence of the minimal values of the ene
 rgy is shown to be ruled by Hamilton-Jacobi equations\, while the minimize
 rs $u(x\,t)$ for the observed images $x$ and smoothing parameters $t$ are 
 given by $u(fx\,t) = x - t \nabla H(\nabla_x E(x\,t))$ where $E(x\,t)$ is
  the minimal value of the energy and $H$ is a Hamiltonian related to the d
 ata fidelity term. Various vanishing smoothing parameter results are deriv
 ed illustrating the role played by the prior in such limits.\n
LOCATION:Seminar Room 1\, Newton Institute
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