Periodic and Spline Multiresolution Analysis and the Lifting Scheme

Abstract

Summary: The lifting scheme is a well-known general framework for theconstruction of wavelets, especially in finite-dimensional settings. After ashort introduction about the basics of lifting, we discuss how waveletconstructions, in two specific finite settings, can be related to thelifting approach. These examples concern, on the one hand, polynomialsplines and, on the other, the Fourier approach for translation-invariantspaces of periodic functions.