[Dottorcomp] Seminari di Matematica Applicata, 06/05/2025, Jürgen Sprekels, Elena Resmerita

[Stefano Lisini]

Seminari di Matematica Applicata, Dipartimento di Matematica "F. Casorati"
e Istituto del CNR IMATI "E. Magenes" di Pavia.

Martedì 6 Maggio 2025, alle *ore 14 precise*, presso l'aula Beltrami del
Dipartimento di Matematica,

Jürgen Sprekels (WIAS Berlin)

terrà un seminario dal titolo:

Optimal control of the viscous Cahn–Hilliard system with hyperbolic
relaxation of the chemical potential,

e alle *ore 15 precise*,

Elena Resmerita (Alpen-Adria University of Klagenfurt)

terrà un seminario dal titolo:

Multiscale hierarchical decomposition in imaging: progress and challenges.

Abstract (Sprekels): We consider the optimal sparse control of a system of
viscous Cahn–Hilliard type in which the chemical potential contains a
hyperbolic relaxation term. Recent results concerning the state system, in
particular, the Fréchet differentiability of the control-to-state operator
in suitable Banach spaces, are reported. For the optimal control problem,
we derive first-order necessary optimality conditions for locally optimal
controls and sparsity results. Finally, we study the asymptotic behavior of
the optimal control problem as the relaxation parameter approaches zero,
showing suitable convergence results for states, optimal controls, and
adjoint states.


Abstract (Resmerita): An important problem in image processing is the image
restoration one,  that is an ill-posed inverse problem which aims to remove
noise and blur from a degraded image. An interesting approach in this
respect was introduced by Tadmor, Nezzar and Vese (2004, 2008), namely the
multiscale hierarchical decomposition method (MHDM). In this presentation,
we first consider MHDM extensions to more general ill-posed problems
affected by additive noise. Then we show how one can adapt the technique to
images corrupted by multiplicative noise and to blind deconvolution
problems. Recall that blind deconvolution is a highly ill-posed nonlinear
inverse problem, which addresses recovering both the true image and the
blur kernel, while little information about the degradation is known. We
point out the advantages of the multiscale hierarchical decomposition
especially when reconstructing images with features at different scales.

-----------------------------------------
https://matematica.unipv.it/ricerca/cicli-di-seminari/seminari-di-matematica-applicata/