1 code implementation • 7 Jun 2022 • Mark A. Iwen, Mark Philip Roach
In this paper we prove that a nonlinear function $f: \mathbb{R}^N \rightarrow \mathbb{R}^{m}$ exists with $m \leq C \left(d / \epsilon^2 \right) \log \left(\frac{\sqrt[d]{V_{\mathcal M}}}{\tau} \right)$ such that $$(1 - \epsilon) \| {\bf x} - {\bf y} \|_2 \leq \left\| f({\bf x}) - f({\bf y}) \right\|_2 \leq (1 + \epsilon) \| {\bf x} - {\bf y} \|_2$$ holds for all ${\bf x} \in \mathcal{M}$ and ${\bf y} \in \mathbb{R}^N$.
no code implementations • 8 Oct 2021 • Mark A. Iwen, Benjamin Schmidt, Arman Tavakoli
Let $\mathcal{M}$ be a smooth $d$-dimensional submanifold of $\mathbb{R}^N$ with boundary that's equipped with the Euclidean (chordal) metric, and choose $m \leq N$.
no code implementations • 17 Jul 2018 • Mark A. Iwen, Felix Krahmer, Sara Krause-Solberg, Johannes Maly
This paper studies the problem of recovering a signal from one-bit compressed sensing measurements under a manifold model; that is, assuming that the signal lies on or near a manifold of low intrinsic dimension.
Information Theory Information Theory