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Approximately dual frames of nonstationary Gabor frames for l 2 ( Z ) and reconstruction errors
Author(s) -
Lian Qiaofang,
You Minghou
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6405
Subject(s) - frame (networking) , mathematics , dual (grammatical number) , constructive , algorithm , computer science , artificial intelligence , process (computing) , telecommunications , art , literature , operating system
Nonstationary Gabor (NSG) frames forL 2 ( R ) allow for flexible sampling and varying window functions and have found applications in adaptive signal analysis. Since any numerical implementation of NSG frames is based on a discrete model, the first author of this paper introduced discrete‐time NSG frames and investigated the existence and construction of NSG frames forl 2 ( Z ) recently. In this paper, we consider the reconstruction of any functions inl 2 ( Z ) from coefficients obtained from NSG frames. Since perfect reconstruction is in general not feasible from NSG frame coefficients, we resort to approximately dual frames and estimate the reconstruction errors. We provide different approximately dual frames of NSG frames under some conditions and give the corresponding reconstruction error bounds. In particular, for a class of NSG frames that are related to painless NSG frames, we show that the approximately dual frames carry the NSG structure. Finally, a constructive example is given to illustrate the theoretical results.