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SUMMARY:The Accuracy-Stability Trade-Off and Sharp Bounds in Inverse Probl
 ems - Nina M. Gottschling (Oak Ridge National Laboratory)
DTSTART:20260430T140000Z
DTEND:20260430T150000Z
UID:TALK246622@talks.cam.ac.uk
CONTACT:Georg Maierhofer
DESCRIPTION:This seminar presents computable sharp accuracy bounds for inv
 erse problems and their applications to single-molecule fluorescence micro
 scopy and super-resolution of multispectral satellite data.\n\nInverse pro
 blems - recovering unknown quantities from noisy measurements - arise in f
 ields such as medical imaging\, radar\, microscopy\, and astronomy. These 
 problems are often ill-posed and are approximately solved using methods ra
 nging from optimization (e.g.\, compressed sensing) over Bayesian approach
 es to deep learning based inverse maps. We discuss the fundamental accurac
 y–stability tradeoff [Gottschling et al.\, SIAM Review (2025)] and [Colb
 rook et al.\, PNAS (2022)]\, which implies nonzero limits on reconstructio
 n accuracy for all stable inverse methods. While these theoretical limits 
 exist\, they are generally not computable. Given the myriads of available 
 methods to solve inverse problems\, existing approaches and frameworks lac
 k universal\, practical bounds that can guide method selection across inve
 rse problems. \n\nWe introduce computable\, method-independent sharp accur
 acy bounds that depend only on the signal dataset\, forward model\, and no
 ise model of the inverse problem. An accompanying algorithmic framework an
 d code make these bounds practically applicable. The approach is validated
  on fluorescence localization microscopy and multispectral satellite super
 -resolution\, enabling optimization of data acquisition and system design 
 before developing inverse reconstruction methods.
LOCATION:Centre for Mathematical Sciences\, MR14
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