Multiresolution Approximation Using Shifted Splines
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.
- URL: http://bigwww.epfl.ch/publications/mueller9801.ps
- URL: http://bigwww.epfl.ch/publications/mueller9801.html
Keywords: Shifted Splines
Record created on 2005-11-30, modified on 2016-08-08