Seminar Scientific Computing (Markus Pohlmann, Georg-August-Universität Göttingen)
Minimax detection of frame-based signals in statistical inverse problems
|Date:||06/16/2021, 2:00 PM - 3:00 PM|
|Location:||zoom video conference|
|Organizer:||Lehrstuhl für Mathematik IX (Wissenschaftliches Rechnen)|
In the summer semester 2021, the lectures will take place as Zoom video conferences, Wednesdays at 14:00.
We start this talk by giving a brief overview of the core ideas of testing and minimax distinguishability.
Afterwards, we focus on linear inverse problems with Gaussian white noise. In this setting, we provide asymptotic upper and lower bounds for the minimax detection threshold of signals which are members of certain collections of frame vectors. The thresholds will be characterized in terms of the redundancy of the frame and the degree of ill-posedness of the inverse problem corresponding to the forward operator. We are especially interested in nding combinations of signals and operators for which sharp thresholds can be derived, which means that the upper and lower bounds coincide.
Finally, we discuss our results for the example of the 2D Radon transform.
via Zoom video conference (request the Zoom link from email@example.com)
All lectures in the 'Seminar Scientific Computing'