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E. S. Ottosen and M. Nielsen. A characterization of sparse nonstationary Gabor expansions. Journal of Fourier Analysis and Applications, 24(4):1048–1071, Springer, 2018.
We investigate the problem of constructing sparse time--frequency representations with flexible frequency resolution, studying the theory of nonstationary Gabor frames (NSGFs) in the framework of decomposition spaces. Given a painless NSGF, we construct a compatible decomposition space and prove that the NSGF forms a Banach frame for the decomposition space. Furthermore, we show that the decomposition space norm can be completely characterized by a sparseness condition on the frame coefficients and we prove an upper bound on the approximation error occurring when thresholding the frame coefficients for signals belonging to the decomposition space.
@article{00b91cc492fe4640b931611c824c8997,
Abstract = {We investigate the problem of constructing sparse time--frequency representations with flexible frequency resolution, studying the theory of nonstationary Gabor frames (NSGFs) in the framework of decomposition spaces. Given a painless NSGF, we construct a compatible decomposition space and prove that the NSGF forms a Banach frame for the decomposition space. Furthermore, we show that the decomposition space norm can be completely characterized by a sparseness condition on the frame coefficients and we prove an upper bound on the approximation error occurring when thresholding the frame coefficients for signals belonging to the decomposition space.},
Author = {Ottosen, {E. S.} and Nielsen, M.},
Bib2Html_Dl_Html = {http://dx.doi.org/10.1007/s00041-017-9546-6},
Bib2Html_Pubtype = {Journal Article},
Date-Added = {2019-03-04 14:53:15 +0100},
Date-Modified = {2019-03-04 15:16:55 +0100},
Issn = {1069-5869},
Journal = {Journal of Fourier Analysis and Applications},
Keywords = {Time-frequency analysis, nonstationary Gabor frames, Decomposition spaces, Banach frames, Nonlinear approximation},
Language = {English},
Number = {4},
Pages = {1048--1071},
Publisher = {Springer},
Title = {A characterization of sparse nonstationary Gabor expansions},
Volume = {24},
Year = {2018},
Bdsk-Url-1 = {https://doi.org/10.1007/s00041-017-9546-6}}
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