The Accuracy-Stability Trade-Off and Sharp Bounds in Inverse Problems

This seminar presents computable sharp accuracy bounds for inverse problems and their applications to single-molecule fluorescence microscopy and super-resolution of multispectral satellite data.

Inverse problems – recovering unknown quantities from noisy measurements – arise in fields such as medical imaging, radar, microscopy, and astronomy. These problems are often ill-posed and are approximately solved using methods ranging from optimization (e.g., compressed sensing) over Bayesian approaches to deep learning based inverse maps. We discuss the fundamental accuracy–stability tradeoff [Gottschling et al., SIAM Review (2025)] and [Colbrook et al., PNAS (2022)], which implies nonzero limits on reconstruction 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 lack universal, practical bounds that can guide method selection across inverse problems.

We introduce computable, method-independent sharp accuracy bounds that depend only on the signal dataset, forward model, and noise model of the inverse problem. An accompanying algorithmic framework and 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.

• Speaker: Nina M. Gottschling (Oak Ridge National Laboratory)
• Thursday 30 April 2026, 15:00–16:00
• Venue: Centre for Mathematical Sciences, MR14.
• Series: Applied and Computational Analysis; organiser: Georg Maierhofer.