| Date | Speaker | Topic |
|---|---|---|
| January 16 | Organizational Meeting |
Organizational Meeting
. |
| January 23 |
TBA |
TBA Abstract: TBA . |
| January 30 |
TBA |
TBA Abstract: TBA . |
| February 6 | TBA |
TBA Abstract: TBA |
| February 13 |
TBA |
TBA Abstract: TBA . |
| February 20 |
Martin Schmoll, Clemson University |
Probabilistic Frames and Wasserstein Distances Abstract: We take a look at probabilistic frames from the perspective of Wasserstein distances. The frame condition can be captured using Wasserstein distances, hence Wasserstein distances appear naturally in the theory of probabilistic frames. Adapting classic results of Olkin and Pukelsheim and an estimate of Gelbrich we analyze probabilistic 2-frames via their frame operator. We deduce Wasserstein optimality of particular linear maps between sets of probabilistic frames with fixed frame operator and apply this insight to extend and simplify some known results. Since Parseval probabilistic frames are path connected, the previous implies that the set of probabilistic frames with any given frame operator is connected. We finally talk about the set of transport duals and some of its generalizations. We show, there are transport duals that cannot be obtained by push-forward. . |
| February 27 |
Cody Stockdale, Clemson University
|
TBA Abstract: TBA . |
| March 6 |
Elodie Ponzi, Saint Louis University andBrett Wick, Washington University Saint Louis |
TBA Abstract: TBA . |
| March 13 | Danny Riley, Tufts University |
TBA Abstract: TBA. . |
| March 20 |
Spring Break |
No Talk Abstract: No Talk . |
| March 27 |
TBA |
TBA Abstract: TBA . |
| April 3 |
TBA |
TBA Abstract: TBA . |
| April 10 |
Richard Huber, Technical University of Denmark |
The L2-Optimal Discretization of Tomographic Projection Operators Abstract: Tomographic inverse problems are a cornerstone of medical investigations, allowing the visualization of patients’ interior features. While the infinite-dimensional operators modeling the measurement process (e.g., the Radon transform) are well understood, in practice one can only observe finitely many measurements and employ finitely many computations in reconstruction. Thus, proper discretization of these operators is crucial; principle criteria are the approximation quality (discretization error) and the computational complexity. For iterative reconstruction approaches, the computation of the forward operator and the adjoint (called the backprojection) is often a major driver of the methods’ computational complexity. Different discretization approaches show distinct strengths regarding the approximation quality of the forward- or backward projections, respectively, which commonly leads to the use of the ray-driven forward and the pixel-driven backprojection (creating a non-adjoint pair of operators). Using such unmatched projection pairs in iterative methods can be problematic, as theoretical convergence guarantees of many iterative methods are based on matched operators. We present a novel theoretical framework for designing an L2-optimal Galerkin discretization of the forward projection. Curiously, this optimized scheme is also the optimal discretization for the backprojection. In particular, this approach grants a matched discretization framework for which both the forward and backward discretization (being the optimal choices) converge in the strong operator topology, thus eliminating the need for unmatched operator pairs. In the parallel beam case, this optimal discretization is the well-known strip model for discretization, while in the fanbeam case, a novel weighted strip model is optimal. . |
| April 17 |
Martin Buck, Tufts University |
TBA Abstract: TBA . |
| April 24 |
TBA |
TBA Abstract: TBA . |