Minimum support interpolators with optimum approximation properties
- 27 November 2002
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- Vol. 3, 242-245
- https://doi.org/10.1109/icip.1998.999014
Abstract
We investigate the functions of given approximation order L that have the smallest support. Those are shown to be linear combinations of the B-spline of degree L-1 and its L-1 first derivatives. We then show how to find the functions that minimize the asymptotic approximation constant among this finite dimension space; in particular, a tractable induction relation is worked out. Using these functions instead of splines, we observe that the approximation error is dramatically reduced, not only in the limit when the sampling step tends to zero, but also for higher values up to the Shannon rate. Finally, we show that those optimal functions satisfy a scaling equation, although less simple than the usual two-scale difference equation.Keywords
This publication has 6 references indexed in Scilit:
- Quantitative L/sup 2/ error analysis for interpolation methods and wavelet expansionsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- Approximation Error for Quasi-Interpolators and (Multi-)Wavelet ExpansionsApplied and Computational Harmonic Analysis, 1999
- On the approximation power of convolution-based least squares versus interpolationIEEE Transactions on Signal Processing, 1997
- Approximation power of biorthogonal wavelet expansionsIEEE Transactions on Signal Processing, 1996
- Convolution-based interpolation for fast, high-quality rotation of imagesIEEE Transactions on Image Processing, 1995
- Sampling procedures in function spaces and asymptotic equivalence with shannon's sampling theoryNumerical Functional Analysis and Optimization, 1994