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Shift-Orthogonal Wavelet Bases Using Splines

M. Unser, P. Thévenaz, A. Aldroubi

IEEE Signal Processing Letters, vol. 3, no. 3, pp. 85-88, March 1996.

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 splines of degree n (odd). The approximation power of these representations is essentially as good as that of the corresponding Battle-Lemarié orthogonal wavelet transform, with the difference that the present wavelet synthesis filters have a much faster decay. This last property, together with the fact that these transformations are almost orthogonal, may be useful for image coding applications.

AUTHOR="Unser, M. and Th{\'{e}}venaz, P. and Aldroubi, A.",
TITLE="Shift-Orthogonal Wavelet Bases Using Splines",
JOURNAL="{IEEE} Signal Processing Letters",

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