Normalized tight vs. general frames in sampling problems. (English) Zbl 1370.42025

Summary: 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.


42C15 General harmonic expansions, frames
94A20 Sampling theory in information and communication theory
15A30 Algebraic systems of matrices
46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)


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