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.


Published in:
IEEE Transactions on Signal Processing, 46, 9, 2555–2558
Year:
1998
Publisher:
IEEE
Keywords:
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 Record created 2005-11-30, last modified 2018-11-14

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