BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Rita Ferreira (King Abdullah University of Science and Technology) DTSTART:20221031T144000Z DTEND:20221031T161000Z DTSTAMP:20260405T174413Z UID:NSCM/73 DESCRIPTION:Title: St ructural changes in nonlocal denoising models arising through bi-level par ameter learning\nby Rita Ferreira (King Abdullah University of Science and Technology) as part of Nečas Seminar on Continuum Mechanics\n\n\nAbs tract\nIn this talk\, we will discuss a unified framework based on bi-leve l optimization schemes to deal with parameter learning in the context of i mage processing. The goal is to identify the optimal regularizer within a family depending on a parameter in a general topological space. Of particu lar interest is the non-compact parameter domains case\, which is relevant \, for instance\, when the commonly used box constraints are disregarded. To overcome this lack of compactness\, we propose a natural extension of t he upper-level functional to the closure of the parameter domain via Gamma -convergence\, which captures possible structural changes in the reconstru ction model at the edge of the domain. Under two main assumptions\, Mosco -convergence of the regularizers and uniqueness of minimizers of the lower -level problem\, we prove that the extension coincides with the relaxation \, thus admitting minimizers that relate to the parameter optimization pro blem of interest. To conclude\, we apply this abstract framework to invest igate four practically relevant models in image denoising\, all featuring nonlocality\; moreover\, the associated families of regularizers exhibit q ualitatively different parameter dependence\, describing a weight factor\, an amount of nonlocality\, an integrability exponent\, and a fractional o rder\, respectively. \nThis talk is based on a joint work with Elisa Davol i\, Carolin Kreisbeck\, and Hidde Schönberger.\n LOCATION:https://researchseminars.org/talk/NSCM/73/ END:VEVENT END:VCALENDAR