Browsing by Author "Lewis, James M."

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    Approximate continuous wavelet transform with an application to noise reduction
    (1998-05-20) Lewis, James M.; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/)
    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 family of compactly-supported orthonormal wavelets), and finally present applications of the transform to denoising and edge detection.
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    The continuous wavelet transform: A discrete approximation
    (1998) Lewis, James M.; Burrus, C. Sidney
    In this thesis, we develop an approximation to the continuous wavelet transform (CWT) which is unique in that it does not require an exact scaling relationship between the levels of the transform, but asymptotically approaches an irrational scaling ratio of 2$\sp{1/n{\sb0}}$ where $n\sb0$ is related to the number of vanishing moments of the original scaling filter. The autocorrelation sequences of the scaling and wavelet filters associated with the Daubechies family of orthonormal compactly supported wavelets are shown to converge to smooth symmetric wavelets which approximate the Deslauriers and Dubuc limiting functions. We show why this transform is superior to a conventional dyadic wavelet transform for the edge detection application, and analyze its performance in denoising applications.