BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Bastian von Harrach (Goethe University Frankfurt) DTSTART:20220407T160000Z DTEND:20220407T170000Z DTSTAMP:20260423T021148Z UID:Inverse/78 DESCRIPTION:Title: Uniqueness and convex reformulation for inverse coefficient problems with finitely many measurements\nby Bastian von Harrach (Goethe University Frankfurt) as part of International Zoom Inverse Problems Seminar\, UC Ir vine\n\n\nAbstract\nSeveral applications in medical imaging and non-destru ctive material testing lead to inverse elliptic coefficient problems\, whe re an unknown coefficient function in an elliptic PDE is to be determined from partial knowledge of its solutions. This is usually a highly non-line ar ill-posed inverse problem\, for which unique reconstructability results \, stability estimates and global convergence of numerical methods are ver y hard to achieve.\n\nIn this talk we will consider an inverse coefficient problem with finitely many measurements and a finite desired resolution. We will present a criterion based on monotonicity\, convexity and localize d potentials arguments that allows us to explicitly estimate the number of measurements that is required to achieve the desired resolution. We also obtain an error estimate for noisy data\, and overcome the problem of loca l minima by rewriting the problem as an equivalent uniquely solvable conve x non-linear semidefinite optimization problem.\n\nReferences\n\nB. Harrac h\, Uniqueness\, stability and global convergence for a discrete inverse e lliptic Robin transmission problem\, Numer. Math. 147 (2021)\, pp. 29-70\, https://doi.org/10.1007/s00211-020-01162-8\n\nB. Harrach\, Solving an inv erse elliptic coefficient problem by convex non-linear semidefinite progra mming\, Optim Lett (2021)\, arXiv preprint (2021)\, https://doi.org/10.100 7/s11590-021-01802-4\n LOCATION:https://researchseminars.org/talk/Inverse/78/ END:VEVENT END:VCALENDAR