no code implementations • 25 Oct 2023 • Elli Karvonen, Matti Lassas, Pekka Pankka, Samuli Siltanen
A novel reconstruction method is introduced for the severely ill-posed inverse problem of limited-angle tomography.
no code implementations • 2 Oct 2022 • Michael Puthawala, Matti Lassas, Ivan Dokmanic, Pekka Pankka, Maarten de Hoop
By exploiting the topological parallels between locally bilipschitz maps, covering spaces, and local homeomorphisms, and by using universal approximation arguments from machine learning, we find that a novel network of the form $\mathcal{T} \circ p \circ \mathcal{E}$, where $\mathcal{E}$ is an injective network, $p$ a fixed coordinate projection, and $\mathcal{T}$ a bijective network, is a universal approximator of local diffeomorphisms between compact smooth submanifolds embedded in $\mathbb{R}^n$.