1 Department of Mathematical Sciences, The Faculty of Engineering and Science, Aalborg University, VBN2 Aalborg University3 IRISA Campus de Beaulieu4 Aalborg University
In this paper we study nonlinear approximation and data representation with redundant function dictionaries. In particular, approximation with redundant wavelet bi-frame systems is studied in detail. Several results for orthonormal wavelets are generalized to the redundant case. In general, for a wavelet bi-frame system the approximation properties are limited by the number of vanishing moments of the system. In some cases this can be overcome by oversampling, but at a price of replacing the canonical expansion by another linear expansion. Moreover, for special non-oversampled wavelet bi-frames we can obtain good approximation properties not restricted by the number of vanishing moments, but again without using the canonical expansion.
I E E E International Conference on Acoustics, Speech and Signal Processing. Proceedings, 2005, Vol 1-5, p. 261-264
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IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005