Articulo
Procrustes problems and Parseval quasi-dual frames
Autor
Corach, Gustavo
Massey, Pedro Gustavo
Ruiz, Mariano Andrés
Institución
Resumen
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. Facultad de Ciencias Exactas