@article{cedfccc131674a769c74464c8b86aedc,
title = "U-invariant sampling and reconstruction in atomic spaces with multiple generators",
abstract = "Given a U-invariant sampling scheme on a Hilbert space H. This paper characterizes atomic subspaces A of H such that every signal χ ∈ 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.",
keywords = "Atomic spaces, pseudoframes, sampling, stationary sequences",
author = "Volker Pohl and Holger Boche",
note = "Funding Information: Manuscript received October 09, 2011; revised February 04, 2012 and March 26, 2012; accepted March 26, 2012. Date of publication April 05, 2012; date of current version June 12, 2012. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Xiang-Gen Xia. This work was supported in part by the German Research Foundation (DFG) by Grant BO 1734/22-1, and by the start-up fund of the TU M{\"u}nchen. Parts of this work were presented at the International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Kyoto, Japan, March 2012.",
year = "2012",
month = jul,
doi = "10.1109/TSP.2012.2193576",
language = "English",
volume = "60",
pages = "3506--3519",
journal = "IEEE Transactions on Signal Processing",
issn = "1053-587X",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "7",
}