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