INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
Procrustes problems and Parseval quasi-dual frames
CORACH, GUSTAVO; PEDRO MASSEY; MARIANO RUIZ
ACTA APPLICANDAE MATHEMATICAE
Lugar: Berlin; Año: 2014 vol. 131 p. 179 - 179
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 ||F X∗ − 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 norms of F X∗ − I, where X is any Parseval frame. The X?s that minimize this quantity are called Parseval quasidual frames of F. Our treatment considers both finite and infinite Parseval quasi-dual frames.