@article{Müller:63053,
title = {Multiresolution Approximation Using Shifted Splines},
author = {Müller, F. and Brigger, P. and Illgner, K. and Unser, M.},
publisher = {IEEE},
journal = {IEEE Transactions on Signal Processing},
number = {9},
volume = {46},
pages = {2555–2558},
year = {1998},
abstract = { We consider the construction of least squares pyramids using shifted polynomial spline basis functions. We derive the pre- and post-filters as a function of the degree n and the shift parameter Δ. We show that the underlying projection operator is entirely specified by two transfer functions acting on the even and odd signal samples, respectively. We introduce a measure of shift-invariance and show that the most favorable configuration is obtained when the knots of the splines are centered with respect to the grid points (i.e., Δ=1/2 when n is odd, and Δ=0 when n is even). The worst case corresponds to the standard multiresolution setting where the spline spaces are nested. },
}