Müller, F.
Brigger, P.
Illgner, K.
Unser, M.
Multiresolution Approximation Using Shifted Splines
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
46
9
Shifted Splines
1998
1998
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.
IEEE
IEEE Transactions on Signal Processing
Journal Articles
10.1109/78.709545