Approximate Continuous Wavelet Transform 
        with an Application to Noise Reduction

        James M. Lewis        C. Sidney Burrus

      Department of Electrical and Computer Engineering
       Rice University, Houston, Texas 77005-1892, USA
             lewi@rice.edu     csb@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.

Paper appears in Proc. ICASSP 98, May 12-15. Seattle, WA.