SHIFT-ORTHOGONAL WAVELET BASES USING SPLINES

We present examples of a new type of wavelet basis functions that are orthogonal across shifts but not across scales. The analysis functions are piecewise linear while the synthesis functions are polynomial spl ines of degree n (odd). The approximation power of these representatio ns is essentially as good as that of the corresponding Battle-Lemarie orthogonal wavelet transform, with the difference that the present wav elet synthesis filters have a much faster decay. This last property, t ogether with the fact that these transformations are almost orthogonal , may be useful for image coding applications.