Open Access
Spring 2017 Normalized tight vs. general frames in sampling problems
Tomaž Košir, Matjaž Omladič
Adv. Oper. Theory 2(2): 114-125 (Spring 2017). DOI: 10.22034/aot.1611-1063


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.


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Tomaž Košir. Matjaž Omladič. "Normalized tight vs. general frames in sampling problems." Adv. Oper. Theory 2 (2) 114 - 125, Spring 2017.


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

zbMATH: 1370.42025
MathSciNet: MR3730063
Digital Object Identifier: 10.22034/aot.1611-1063

Primary: 47N99
Secondary: 15A30 , 46C05 , 94A20

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

Rights: Copyright © 2017 Tusi Mathematical Research Group

Vol.2 • No. 2 • Spring 2017
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