30.11.2022 um 14:15 Uhr in 69/125
Paul Catala (Universität Osnabrück)
Efficiently solving semidefinite relaxations for optimal transport
In this talk, I will discuss a new solver for optimal transport problems on the torus, based on Lasserre's hierarchies. I will show how the original problem can be approximated by a hierarchy of semidefinite programs (SDP) involving only moments of the measures. I will then discuss how one can leverage the particular structure of the solutions to design an efficient solver for these SDP. I will end by describing an extension of Prony's method to recover non-discrete measures from the moment sequences outputted by the previous semidefinite optimization.
07.12.2022 um 14:15 Uhr in 69/125
Tarek Emmrich (Universität Osnabrück)
Sparse recovery on graphs and sufficient conditions for success
We present methods to recover signals on graphs that have a sparse representation in the basis of Laplacian eigenvectors. We give sufficient algebraic conditions on the characteristic polynomial for the success of the methods. This will also lead to a new uncertainty principle for the graph Fourier transform of those graphs. We end by discussing the relation to Chebotarev's famous theorem that all minors of Fourier matrices of prime order do not vanish.
11.01.2023 um 14:15 Uhr in 69/125
Manuel Twent (Universität Osnabrück)
Kettenbrüche und ihre Verbindung zur Dispersion von 2d-Gittern
18.01.2023 um 14:15 Uhr in 69/125
Kumar Harsha (Universität Osnabrück)
Data compression using Lattice rules
The mean squared error is one of the standard loss functions in supervised machine learning. However, computing this loss for enormous data sets can be computationally demanding. We present methods to reduce large data sets to a smaller size using rank-1 lattice rules. With this reduction strategy in the pre-processing step, every lattice point gets a weight representing the original data making iterative loss calculations faster.
25.01.2023 um 14:15 Uhr in 69/125
Mathias Hockmann (Universität Osnabrück)
Sparse super resolution and the diffraction limit
In microscopy applications, numerous definitions of the term “resolution limit” or “diffraction
limit” exist. While they have the common reasoning to describe the smallest resolvable distance
between two objects, they differ by a constant and lack in a clear definition of what is meant
by resolvability. We address this issue by considering super resolution (SR) as the mapping of
Fourier coefficients of a discrete measure on [0, 1) d to its support and weights. In practice, the
question of resolvability is then linked to the condition number of this map. The diffraction
limit can be seen as an assumption on the separation of the involved measures similar to the
Rayleigh criterion. In fact, we can prove that SR is well-conditioned if the Rayleigh criterion
holds and this improves a bound on the assumed separation by Chen and Moitra. This is joint
work with Stefan Kunis.