Advances in Operator Theory

Normalized tight vs. general frames in sampling problems

Tomaž Košir and Matjaž Omladič

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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

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

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

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Zentralblatt MATH identifier

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

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


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.

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