Details
| Original language | English |
|---|---|
| Pages (from-to) | 727-742 |
| Number of pages | 16 |
| Journal | Discrete and Computational Geometry |
| Volume | 56 |
| Issue number | 3 |
| Publication status | Published - 1 Oct 2016 |
Abstract
Hilbert space frames generalize orthonormal bases to allow redundancy in representations of vectors while keeping good reconstruction properties. A frame comes with an associated frame operator encoding essential properties of the frame. We study a polytope that arises in an algorithm for constructing all finite frames with given lengths of frame vectors and spectrum of the frame operator, which is a Gelfand–Tsetlin polytope. For equal norm tight frames, we give a non-redundant description of the polytope in terms of equations and inequalities. From this we obtain the dimension and number of facets of the polytope. While studying the polytope, we find two affine isomorphisms and show how they relate to operations on the underlying frames.
Keywords
- Combinatorics, Convex geometry, Hilbert space frames, Polytopes
ASJC Scopus subject areas
- Mathematics(all)
- Theoretical Computer Science
- Mathematics(all)
- Geometry and Topology
- Mathematics(all)
- Discrete Mathematics and Combinatorics
- Computer Science(all)
- Computational Theory and Mathematics
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In: Discrete and Computational Geometry, Vol. 56, No. 3, 01.10.2016, p. 727-742.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Polytopes of Eigensteps of Finite Equal Norm Tight Frames
AU - Haga, Tim
AU - Pegel, Christoph
N1 - Publisher Copyright: © 2016, Springer Science+Business Media New York. Copyright: Copyright 2016 Elsevier B.V., All rights reserved.
PY - 2016/10/1
Y1 - 2016/10/1
N2 - Hilbert space frames generalize orthonormal bases to allow redundancy in representations of vectors while keeping good reconstruction properties. A frame comes with an associated frame operator encoding essential properties of the frame. We study a polytope that arises in an algorithm for constructing all finite frames with given lengths of frame vectors and spectrum of the frame operator, which is a Gelfand–Tsetlin polytope. For equal norm tight frames, we give a non-redundant description of the polytope in terms of equations and inequalities. From this we obtain the dimension and number of facets of the polytope. While studying the polytope, we find two affine isomorphisms and show how they relate to operations on the underlying frames.
AB - Hilbert space frames generalize orthonormal bases to allow redundancy in representations of vectors while keeping good reconstruction properties. A frame comes with an associated frame operator encoding essential properties of the frame. We study a polytope that arises in an algorithm for constructing all finite frames with given lengths of frame vectors and spectrum of the frame operator, which is a Gelfand–Tsetlin polytope. For equal norm tight frames, we give a non-redundant description of the polytope in terms of equations and inequalities. From this we obtain the dimension and number of facets of the polytope. While studying the polytope, we find two affine isomorphisms and show how they relate to operations on the underlying frames.
KW - Combinatorics
KW - Convex geometry
KW - Hilbert space frames
KW - Polytopes
UR - http://www.scopus.com/inward/record.url?scp=84976415962&partnerID=8YFLogxK
U2 - 10.1007/s00454-016-9799-x
DO - 10.1007/s00454-016-9799-x
M3 - Article
VL - 56
SP - 727
EP - 742
JO - Discrete and Computational Geometry
JF - Discrete and Computational Geometry
SN - 0179-5376
IS - 3
ER -