%0 Journal Article
%T Normalized tight vs. general frames in sampling problems
%J Advances in Operator Theory
%I Tusi Mathematical Research Group (TMRG)
%Z 2538-225X
%A Košir, Tomaž
%A Omladič, Matjaž
%D 2017
%\ 04/01/2017
%V 2
%N 2
%P 114-125
%! Normalized tight vs. general frames in sampling problems
%K Sampling theory
%K consistent and quasiconsistent reconstructions
%K frames and normalized tight frames
%K replacement operator
%K several samples
%R 10.22034/aot.1611-1063
%X 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.
%U http://www.aot-math.org/article_43335_a0eb80054183c1d231c2f48925a39cca.pdf