Nonlinear approximation schemes associated with nonseparable wavelet bi-frames |
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Authors: | Martin Ehler |
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Affiliation: | aDepartment of Mathematics, University of Maryland, College Park, MD 20742-4015, USA;bDepartment of Mathematics and Computer Science, Philipps-Universität Marburg, Hans-Meerwein Str., 35032 Marburg, Germany |
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Abstract: | In the present paper, we study nonlinear approximation properties of multivariate wavelet bi-frames. For a certain range of parameters, the approximation classes associated with best N-term approximation are determined to be Besov spaces and thresholding the wavelet bi-frame expansion realizes the approximation rate. Our findings extend results about dyadic wavelets to more general scalings. Finally, we verify that the required linear independence assumption is satisfied for particular families of nondyadic wavelet bi-frames in arbitrary dimensions. |
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Keywords: | Wavelet bi-frame Besov spaces Nonlinear approximation Jackson inequality Bernstein inequality Isotropic scaling |
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