Minimum support interpolators with optimum approximation properties
Journal
IEEE International Conference on Image Processing
Journal Volume
3
Date Issued
1998-12-01
Author(s)
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 minimizes the asymptotic approximation constant among this finite dimension space; in particular, a tractable induction relation is worked out. Using these functions instead of splices, we observe that the approximation error is dramatically reduced, but 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 these optimal functions satisfy a scaling equations, although less simple than the usual two-scale difference equation.
Type
conference paper