Covering point-sets with parallel hyperplanes and sparse signal recovery
| Autor: | Lenny Fukshansky, Alexander Hsu |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Computational Theory and Mathematics
Mathematics - Metric Geometry 52C17 05B40 94A12 FOS: Mathematics Discrete Mathematics and Combinatorics Mathematics - Combinatorics Metric Geometry (math.MG) Geometry and Topology Combinatorics (math.CO) Numerical Analysis (math.NA) Mathematics - Numerical Analysis Theoretical Computer Science |
| Popis: | We give a new deterministic construction of integer sensing matrices that can be used for the recovery of integer-valued signals in compressed sensing. This is a family of $n \times d$ integer matrices, $d \geq n$, with bounded sup-norm and the property that no $\ell$ column vectors are linearly dependent, $\ell \leq n$. Further, if $\ell \leq o(\log n)$ then $d/n \to \infty$ as $n \to \infty$. Our construction comes from particular sets of difference vectors of point-sets in $\mathbb R^n$ that cannot be covered by few parallel hyperplanes. We construct examples of such sets on the $0, \pm 1$ grid and use them for the matrix construction. We also show a connection of our constructions to a simple version of the Tarski plank problem. 11 pages, 1 figure; to appear in Discrete and Computational Geometry |
| Databáze: | OpenAIRE |
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