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U-Invariant Sampling and Reconstruction in Atomic Spaces With Multiple Generators

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2 Author(s)
Volker Pohl ; Lehrstuhl für Theoretische Informationstechnik, Technische Universität München, München, Germany ; Holger Boche

Given a U-invariant sampling scheme on a Hilbert space H. This paper characterizes atomic subspaces A of H such that every signal xA can be reconstructed from its generalized samples acquired with the U-invariant sampling scheme. If signal recovery is possible a linear filter is derived which reconstructs the signal from the samples. Moreover, the paper gives necessary and sufficient conditions on a sequence of sampling functions such that it forms a pseudoframe or pseudo-Riesz basis for a given atomic subspace A.

Published in:

IEEE Transactions on Signal Processing  (Volume:60 ,  Issue: 7 )