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