BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Carola-Bibiane Schönlieb (University of Cambridge) DTSTART:20210629T101500Z DTEND:20210629T114500Z DTSTAMP:20260423T022602Z UID:MathDeep/11 DESCRIPTION:Title: Deeply learned regularisation for inverse problems\nby Carola-Bibian e Schönlieb (University of Cambridge) as part of Mathematics of Deep Lear ning\n\n\nAbstract\nInverse problems are about the reconstruction of an un known physical quantity from indirect measurements. In imaging\, they appe ar in a variety of places\, from medical imaging\, for instance MRI or CT\ , to remote sensing\, for instance Radar\, to material sciences and molecu lar biology\, for instance electron microscopy. Here\, imaging is a tool f or looking inside specimen\, resolving structures beyond the scale visible to the naked eye\, and to quantify them. It is a mean for diagnosis\, pre diction and discovery.\nMost inverse problems of interest are ill-posed an d require appropriate mathematical treatment for recovering meaningful sol utions. Classically\, inversion approaches are derived almost conclusively in a knowledge driven manner\, constituting handcrafted mathematical mode ls. Examples include variational regularization methods with Tikhonov regu larisation\, the total variation and several sparsity-promoting regularize rs such as the L1 norm of Wavelet coefficients of the solution. While such handcrafted approaches deliver mathematically rigorous and computationall y robust solutions to inverse problems\, they are also limited by our abil ity to model solution properties accurately and to realise these approache s in a computationally efficient manner.\nRecently\, a new paradigm has be en introduced to the regularisation of inverse problems\, which derives re gularised solutions to inverse problems in a data driven way. Here\, the i nversion approach is not mathematically modelled in the classical sense\, but modelled by highly over-parametrised models\, typically deep neural ne tworks\, that are adapted to the inverse problems at hand by appropriately selected (and usually plenty of) training data. Current approaches that f ollow this new paradigm distinguish themselves through solution accuracies paired with computational efficieny that were previously unconceivable.\n In this talk I will provide a glimpse into such deep learning approaches a nd some of their mathematical properties. I will finish with open problems and future research perspectives.\n LOCATION:https://researchseminars.org/talk/MathDeep/11/ END:VEVENT END:VCALENDAR