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...
Guardado en:
| Autores principales: | , , |
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| Formato: | Articulo Preprint |
| Lenguaje: | Inglés |
| Publicado: |
2014
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| Materias: | |
| 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: |
| Sumario: | 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. |
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