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Approximate continuous wavelet transform with an application to noise reduction

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2 Author(s)
Lewis, J.M. ; Dept. of Electr. & Comput. Eng., Rice Univ., Houston, TX, USA ; Burrus, C.S.

We describe a generalized scale-redundant wavelet transform which approximates a dense sampling of the continuous wavelet transform (CWT) in both time and scale. The dyadic scaling requirement of the usual wavelet transform is relaxed in favor of an approximate scaling relationship which in the case of a Gaussian scaling function is known to be asymptotically exact and irrational. This scheme yields an arbitrarily dense sampling of the scale axis in the limit. Similar behavior is observed for other scaling functions with no explicit analytic form. We investigate characteristics of the family of Lagrange interpolating filters (related to the Daubechies (1988) family of compactly-supported orthonormal wavelets), and finally present applications of the transform to denoising and edge detection

Published in:

Acoustics, Speech and Signal Processing, 1998. Proceedings of the 1998 IEEE International Conference on  (Volume:3 )

Date of Conference:

12-15 May 1998