Mathematics of Data Science

Learned model-based reconstructions for inverse problems: robustness and convergence guarantees

Speaker: Andreas Hauptmann (University of Oulo)
Location: Building 303A Aud. 43, DTU Lyngby Campus

Abstract:
In recent years, deep learning has achieved remarkable empirical success for image reconstruction. This has catalysed an ongoing quest for the precise characterization of the correctness and reliability of data-driven methods in critical use cases, for instance, in medical imaging. Notwithstanding the excellent performance and efficacy of deep learning-based methods, concerns have been raised regarding the approaches’ stability, or lack thereof, with serious practical implications. Significant advances have been made in recent years to unravel the inner workings of data-driven image recovery methods, challenging their widely perceived black-box nature.

In this talk, I will give an overview of common learned model-based approach in inverse problems. We will discuss relevant notions of robustness and convergence for inverse problems and give examples of models that fall in each category. Specifically, I will challenge the view that learned reconstructions are pure black-box approaches and, in fact, relevant guarantees can also be given in the data-driven world.