Name
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 |
Year | DOI | Venue |
|---|---|---|
1998 | 10.1109/78.709545 | IEEE Transactions on Signal Processing |
Keywords | Field | DocType |
filtering theory,least squares approximations,signal resolution,signal sampling,splines (mathematics),transfer functions,grid points,least squares pyramids,multiresolution approximation,polynomial spline basis functions,post-filters,pre-filters,projection operator,shift invariance,shifted splines,signal samples,transfer functions | Least squares,Spline (mathematics),Mathematical optimization,Invariant (physics),Polynomial,Projection (linear algebra),Multiresolution analysis,Basis function,Knot (unit),Mathematics | Journal |
Volume | Issue | ISSN |
46 | 9 | 1053-587X |
Citations | PageRank | References |
7 | 1.47 | 7 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Muller, F. | 1 | 7 | 1.47 |
| Patrick Brigger | 2 | 137 | 9.44 |
| Illgner, K. | 3 | 35 | 4.86 |
| Unser, M. | 4 | 3438 | 442.40 |