Construction of shift-orthogonal wavelets using splines

Michael A. Unser; Philippe Thevenaz; Akram Aldroubi

doi:10.1117/12.255257

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Abstract

We present examples of a new type of wavelet basis functions that are orthogonal across shifts, but not across scales. The analysis functions are low order splines 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- Lemarie 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 transformation s are almost orthogonal, may be useful for image coding and data compression.

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Michael A. Unser, Philippe Thevenaz, and Akram Aldroubi "Construction of shift-orthogonal wavelets using splines", Proc. SPIE 2825, Wavelet Applications in Signal and Image Processing IV, (23 October 1996); doi: 10.1117/12.255257; https://doi.org/10.1117/12.255257

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