The Experts below are selected from a list of 1365 Experts worldwide ranked by ideXlab platform
Carlos Cabrelli - One of the best experts on this subject based on the ideXlab platform.
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time frequency shift invariance and the amalgam balian low theorem
Applied and Computational Harmonic Analysis, 2016Co-Authors: Carlos Cabrelli, Ursula Molter, Gotz E PfanderAbstract:Abstract We consider smoothness properties of the generator of a principal Gabor space on the real line which is invariant under some additional translation–modulation pair. We prove that if a Gabor system on a lattice with rational density is a Riesz basis for its Closed Linear Span, and if the Closed Linear Span, a Gabor space, has any additional translation–modulation invariance, then its generator cannot decay well in time and in frequency simultaneously.
Gotz E Pfander - One of the best experts on this subject based on the ideXlab platform.
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time frequency shift invariance and the amalgam balian low theorem
Applied and Computational Harmonic Analysis, 2016Co-Authors: Carlos Cabrelli, Ursula Molter, Gotz E PfanderAbstract:Abstract We consider smoothness properties of the generator of a principal Gabor space on the real line which is invariant under some additional translation–modulation pair. We prove that if a Gabor system on a lattice with rational density is a Riesz basis for its Closed Linear Span, and if the Closed Linear Span, a Gabor space, has any additional translation–modulation invariance, then its generator cannot decay well in time and in frequency simultaneously.
Ursula Molter - One of the best experts on this subject based on the ideXlab platform.
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time frequency shift invariance and the amalgam balian low theorem
Applied and Computational Harmonic Analysis, 2016Co-Authors: Carlos Cabrelli, Ursula Molter, Gotz E PfanderAbstract:Abstract We consider smoothness properties of the generator of a principal Gabor space on the real line which is invariant under some additional translation–modulation pair. We prove that if a Gabor system on a lattice with rational density is a Riesz basis for its Closed Linear Span, and if the Closed Linear Span, a Gabor space, has any additional translation–modulation invariance, then its generator cannot decay well in time and in frequency simultaneously.
Gitta Kutyniok - One of the best experts on this subject based on the ideXlab platform.
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Fusion frames and distributed processing
Applied and Computational Harmonic Analysis, 2008Co-Authors: Peter G Casazza, Gitta KutyniokAbstract:Let {Wi}i∈I be a (redundant) sequence of subspaces of a Hilbert space each being endowed with a weight vi, and let H be the Closed Linear Span of the Wis, a composite Hilbert space. {(Wi,vi)}i∈I is called a fusion frame provided it satisfies a certain property which controls the weighted overlaps of the subspaces. These systems contain conventional frames as a special case, however they reach far “beyond frame theory.” In case each subspace Wi is equipped with a Spanning frame system {fij}j∈Ji, we refer to {(Wi,vi,{fij}j∈Ji)}i∈I as a fusion frame system. The focus of this article is on computational issues of fusion frame reconstructions, unique properties of fusion frames important for applications with particular focus on those superior to conventional frames, and on centralized reconstruction versus distributed reconstructions and their numerical differences. The weighted and distributed processing technique described in this article is not only a natural fit to distributed processing systems such as sensor networks, but also an efficient scheme for parallel processing of very large frame systems. Another important component of this article is an extensive study of the robustness of fusion frame systems.
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fusion frames and distributed processing
arXiv: Functional Analysis, 2006Co-Authors: Peter G Casazza, Gitta Kutyniok, Shidong LiAbstract:Let $\{W_i\}_{i\in I}$ be a (redundant) sequence of subspaces each being endowed with a weight $v_i$, and let $\mathcal{H}$ be the Closed Linear Span of the $W_i$'s, a composite Hilbert space. Provided that $\{(W_i,v_i)\}_{i \in I}$ satisfies a certain property which controls the weighted overlaps of the subspaces, it is called a {\em fusion frame}. These systems contain conventional frames as a special case, however they go far ``beyond frame theory''. In case each subspace $W_i$ is equipped with a frame system $\{f_{ij}\}_{j \in J_i}$ by which it is Spanned, we refer to $\{(W_i,v_i,\{f_{ij}\}_{j \in J_i})\}_{i \in I}$ as a {\em fusion frame system}. In this paper, we describe a weighted and distributed processing procedure that fuse together information in all subspaces $W_i$ of a fusion frame system to obtain the global information in $\mathcal{H}$. The weighted and distributed processing technique described in fusion frames is not only a natural fit in distributed processing systems such as sensor networks, but also an efficient scheme for parallel processing of very large frame systems. We further provide an extensive study of the robustness of fusion frame systems.
Peter G Casazza - One of the best experts on this subject based on the ideXlab platform.
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Fusion frames and distributed processing
Applied and Computational Harmonic Analysis, 2008Co-Authors: Peter G Casazza, Gitta KutyniokAbstract:Let {Wi}i∈I be a (redundant) sequence of subspaces of a Hilbert space each being endowed with a weight vi, and let H be the Closed Linear Span of the Wis, a composite Hilbert space. {(Wi,vi)}i∈I is called a fusion frame provided it satisfies a certain property which controls the weighted overlaps of the subspaces. These systems contain conventional frames as a special case, however they reach far “beyond frame theory.” In case each subspace Wi is equipped with a Spanning frame system {fij}j∈Ji, we refer to {(Wi,vi,{fij}j∈Ji)}i∈I as a fusion frame system. The focus of this article is on computational issues of fusion frame reconstructions, unique properties of fusion frames important for applications with particular focus on those superior to conventional frames, and on centralized reconstruction versus distributed reconstructions and their numerical differences. The weighted and distributed processing technique described in this article is not only a natural fit to distributed processing systems such as sensor networks, but also an efficient scheme for parallel processing of very large frame systems. Another important component of this article is an extensive study of the robustness of fusion frame systems.
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fusion frames and distributed processing
arXiv: Functional Analysis, 2006Co-Authors: Peter G Casazza, Gitta Kutyniok, Shidong LiAbstract:Let $\{W_i\}_{i\in I}$ be a (redundant) sequence of subspaces each being endowed with a weight $v_i$, and let $\mathcal{H}$ be the Closed Linear Span of the $W_i$'s, a composite Hilbert space. Provided that $\{(W_i,v_i)\}_{i \in I}$ satisfies a certain property which controls the weighted overlaps of the subspaces, it is called a {\em fusion frame}. These systems contain conventional frames as a special case, however they go far ``beyond frame theory''. In case each subspace $W_i$ is equipped with a frame system $\{f_{ij}\}_{j \in J_i}$ by which it is Spanned, we refer to $\{(W_i,v_i,\{f_{ij}\}_{j \in J_i})\}_{i \in I}$ as a {\em fusion frame system}. In this paper, we describe a weighted and distributed processing procedure that fuse together information in all subspaces $W_i$ of a fusion frame system to obtain the global information in $\mathcal{H}$. The weighted and distributed processing technique described in fusion frames is not only a natural fit in distributed processing systems such as sensor networks, but also an efficient scheme for parallel processing of very large frame systems. We further provide an extensive study of the robustness of fusion frame systems.