Advances in Operator Theory

Normalized tight vs. general frames in sampling problems

Tomaž Košir and Matjaž Omladič

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Abstract

We present a new approach to sampling theory using the operator theory framework. We use a replacement operator and replace general frames of the sampling and reconstruction subspaces by normalized tight frames. The replacement can be done in a numerically stable and efficient way. The approach enables us to unify the standard consistent reconstruction results with the results for quasiconsistent reconstruction. Our approach naturally generalizes to consistent and quasiconsistent reconstructions from several samples. Not only we can handle sampling problems in a more efficient way, we also answer questions that seem to be open so far.

Article information

Source
Adv. Oper. Theory, Volume 2, Number 2 (2017), 114-125.

Dates
Received: 24 November 2016
Accepted: 18 February 2017
First available in Project Euclid: 4 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.aot/1512431560

Digital Object Identifier
doi:10.22034/aot.1611-1063

Mathematical Reviews number (MathSciNet)
MR3730063

Zentralblatt MATH identifier
1370.42025

Subjects
Primary: 47N99: None of the above, but in this section
Secondary: 15A30: Algebraic systems of matrices [See also 16S50, 20Gxx, 20Hxx] 46C05: Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) 94A20: Sampling theory

Keywords
sampling theory consistent and quasiconsistent reconstructions frames and normalized tight frames replacement operator several samples

Citation

Košir, Tomaž; Omladič, Matjaž. Normalized tight vs. general frames in sampling problems. Adv. Oper. Theory 2 (2017), no. 2, 114--125. doi:10.22034/aot.1611-1063. https://projecteuclid.org/euclid.aot/1512431560


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