Periodic and Spline Multiresolution Analysis and the Lifting Scheme

What is it about?

The lifting scheme is a well-known general framework for the construction of wavelets, especially in finitedimensional settings. After a short introduction about the basics of lifting, we discuss how wavelet constructions, in two specific finite settings, can be related to the lifting approach. These examples concern, on the one hand, polynomial splines and, on the other, the Fourier approach for translation-invariant spaces of periodic functions.

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