Procrustes problems and Parseval quasi-dual frames

Parseval frames have particularly useful properties, and in some cases, they can be used to reconstruct signals which were analyzed by a non-Parseval frame. In this paper, we completely describe the degree to which such reconstruction is feasible. Indeed, notice that for fixed frames F and X wit...

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Detalles Bibliográficos
Autores principales: Corach, Gustavo, Massey, Pedro Gustavo, Ruiz, Mariano Andrés
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2014
Materias:
Matemática
Procrustes problems
Parseval frames
Dual frames
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/102245
https://ri.conicet.gov.ar/11336/12166
http://link.springer.com/article/10.1007/s10440-013-9853-0
https://arxiv.org/abs/1309.7914
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-102245
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Procrustes problems
Parseval frames
Dual frames
spellingShingle Matemática
Procrustes problems
Parseval frames
Dual frames
Corach, Gustavo
Massey, Pedro Gustavo
Ruiz, Mariano Andrés
Procrustes problems and Parseval quasi-dual frames
topic_facet Matemática
Procrustes problems
Parseval frames
Dual frames
description Parseval frames have particularly useful properties, and in some cases, they can be used to reconstruct signals which were analyzed by a non-Parseval frame. In this paper, we completely describe the degree to which such reconstruction is feasible. Indeed, notice that for fixed frames F and X with synthesis operators F and X, the operator norm of FX∗−I measures the (normalized) worst-case error in the reconstruction of vectors when analyzed with X and synthesized with F . Hence, for any given frame F , we compute explicitly the infimum of the operator norm of FX∗−I, where X is any Parseval frame. The X ’s that minimize this quantity are called Parseval quasi-dual frames of F . Our treatment considers both finite and infinite Parseval quasi-dual frames.
format Articulo
Preprint
author Corach, Gustavo
Massey, Pedro Gustavo
Ruiz, Mariano Andrés
author_facet Corach, Gustavo
Massey, Pedro Gustavo
Ruiz, Mariano Andrés
author_sort Corach, Gustavo
title Procrustes problems and Parseval quasi-dual frames
title_short Procrustes problems and Parseval quasi-dual frames
title_full Procrustes problems and Parseval quasi-dual frames
title_fullStr Procrustes problems and Parseval quasi-dual frames
title_full_unstemmed Procrustes problems and Parseval quasi-dual frames
title_sort procrustes problems and parseval quasi-dual frames
publishDate 2014
url http://sedici.unlp.edu.ar/handle/10915/102245
https://ri.conicet.gov.ar/11336/12166
http://link.springer.com/article/10.1007/s10440-013-9853-0
https://arxiv.org/abs/1309.7914
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AT ruizmarianoandres procrustesproblemsandparsevalquasidualframes
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