Nonlinear approximation schemes associated with nonseparable wavelet bi-frames

Authors:
Martin Ehler
Affiliations:
Department of Mathematics, University of Maryland, College Park, MD 20742-4015, USA and Department of Mathematics and Computer Science, Philipps-Universität Marburg, Hans-Meerwein Str., 35032 ...
Venue:
Journal of Approximation Theory
Year:
2009

Citing 3
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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.