EPFL | Biomedical Imaging Group | Shift-Orthogonal Wavelets

Construction of Shift-Orthogonal Wavelets Using Splines

M. Unser, P. Thévenaz, A. Aldroubi

Proceedings of the SPIE Conference on Mathematical Imaging: Wavelet Applications in Signal and Image Processing IV, Denver CO, USA, August 6-9, 1996, vol. 2825, part I, pp. 465–473.

We present examples of a new type of wavelet basis function that are orthogonal across shifts, but not across scales. The analysis functions are low order splines (piecewise constant or linear) while the synthesis functions are polynomial splines of higher degree n₂. 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 and data compression.

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