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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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