[Dottorcomp] Seminari di Matematica Applicata. Lunedì 3 aprile. Konstantinos Bessas.

[Stefano Lisini]

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

Lunedì 3 aprile 2023, alle ore 15.00 precise, presso l'aula Beltrami del
Dipartimento di Matematica,

Konstantinos Bessas (Università di Pavia)

terrà un seminario dal titolo:

Nonlocal total variation denoising model with weighted L^1 fidelity.

Il seminario verrà anche trasmesso in diretta su zoom.

Link Zoom:

https://us02web.zoom.us/j/84698161312?pwd=MzlvZWJIcTQ0ZWppVHVOOU1QemZiZz09

Abstract.
Image denoising is a core problem in image processing: it consists in
finding an approximation of a distorted image which is at the same time
more regular. The competition between fidelity and regularity endows
the problem with a natural variational structure, which gave rise to a
broad investigation of minimization-based denoising models.
In particular, in the last years, more and more attention was given to
nonlocal
ones.
In this talk I will present a general class of nonlocal denoising models,
whose regularizing term is a nonlocal variation induced by a suitable
(non-integrable) kernel K, and the fidelity term is given by the L^1 norm
with respect to an absolutely continuous measure with positively
lower-bounded L^∞ density.
I will discuss existence and uniqueness of solutions and regularity of
their level sets, both for high and low values of the fidelity parameter.
Finally, I will analyse in detail the fidelity of the model in the case of
binary data given by the characteristic functions of convex sets. Part of
the results that I will present were obtained in collaboration with Giorgio
Stefani (SISSA, Trieste).


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