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

作者：Pohl Volker^*; Boche Holger

来源：IEEE Transactions on Signal Processing, 2012, 60(7): 3506-3519.

DOI：10.1109/TSP.2012.2193576

• Atomic spaces
• pseudoframes
• sampling
• stationary sequences

Given a U-invariant sampling scheme on a Hilbert space H. This paper characterizes atomic subspaces A of H such that every signal x is an element of A 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.

• 出版日期2012-7