On Convex FiniteDimensional Variational Methods in Imaging Sciences, and HamiltonJacobi Equations
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If you have a question about this talk, please contact Mustapha Amrani.
Inverse Problems
We consider standard finitedimensional variational models used in signal/image processing that consist in minimizing an energy involving a data fidelity term and a regularization term. We propose new remarks from a theoretical perspective which give a precise description on how the solutions of the optimization problem depend on the amount of smoothing effects and the data itself. The dependence of the minimal values of the energy is shown to be ruled by HamiltonJacobi equations, while the minimizers $u(x,t)$ for the observed images $x$ and smoothing parameters $t$ are given by $u(fx,t) = x – t
abla H(
abla_x E(x,t))$ where $E(x,t)$ is the minimal value of the energy and $H$ is a Hamiltonian related to the data fidelity term. Various vanishing smoothing parameter results are derived illustrating the role played by the prior in such limits.
This talk is part of the Isaac Newton Institute Seminar Series series.
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