Constructions of Dual Frames Compensating for Erasures with Implementation

pregledni rad (znanstveni)

pregledni rad (znanstveni)

Constructions of Dual Frames Compensating for Erasures with Implementation

Vrsta prilog u knjizi
Tip pregledni rad (znanstveni)
Godina 2024
Nadređena publikacija Extended Abstracts 2022 : Proceedings of the 7th International Conference on the Anthropological Theory of the Didactic (CITAD7)
Stranice str. 27-36
DOI 10.1007/978-3-031-57005-6_4
EISSN 2297-024X
Status objavljeno

Sažetak

Let $Isubseteq Bbb N$ be a finite or infinite set. Let $(x_n)_{ninBbb N}$ be a frame for a Hilbert space $H$ and $E$ a finite set of indices which satisfies the minimal redundancy condition. There are several ways how to, starting from an arbitrary dual frame $(y_n)_{ninBbb N}$ of $(x_n)_{ninBbb N}$, compute a dual frame of the reduced frame $(x_n)_{nin E^c}$ which is then used for perfect reconstruction from preserved frame coefficients.
In this paper we implemented the algorithms for a method of a perfect reconstruction based on iterative procedures and tested them for computational efficiency.

Ključne riječi

Frame; Erasure; Reconstruction; Dual frame; Canonical dual