Discrete finite variation: a new measure of smoothnessfor the
  		design of wavelet basis

	 Jan E. Odegard     C. Sidney Burrus

   Department of Electrical and Computer Engineering
      Rice University, Houston, TX 77251-1892, USA
          odegard@rice.edu        csb@rice.edu


A new method for measuring and designing smooth wavelet basis which
dispenses with the need for having a large number of zero moments of
the wavelet is given. The method is based on minimizing the ``discrete
finite variation'', and is a measure of the local ``roughness'' of a
\emph{sampled} version of the scaling function giving rise to
``visually smooth'' wavelet basis.  Smooth wavelet basis are deemed to
be important for several applications and in particularly for image
compression where the goal is to limit spurious artifacts due to
non-smooth basis functions in the presence of quantization of the
individual subbands.  The definition of smoothness introduced here
gives rise to new algorithms for designing smooth wavelet basis with
only one vanishing moment leaving free parameters, otherwise used for
setting moments to zero, for optimization.

Paper appears in Proc. ICASSP-96, Atlanta, GA.