Bivariate cardinal spline functions for digital signal processing. (English) Zbl 1112.94308

Kopotun, Kirill (ed.) et al., Trends in approximation theory. Papers from the internatinal symposium in honor of the 60th birthday of Larry L. Schumaker, Nashville, TX, USA, May 17–20, 2000. Nashville, TX: Vanderbilt University Press (ISBN 0-8265-1379-4/hbk). Innovations in Applied Mathematics, 261-272 (2001).
Summary: We investigate the applicability of multivariate spline functions in digital signal processing. We offer a new technique for resampling two-dimensional discrete data using bivariate cardinal splines which are linear combinations of B-splines. We construct bivariate cardinal splines with a number of desirable features, which make them useful for image processing. One of these features is that the coefficients of the interpolating bivariate cardinal splines are the sample data at the interpolation points. The interpolants converge uniformly to the function being interpolated, as the sampling increment approaches zero. Compared to the popular tensor product construction, with the same degree of smoothness, our bivariate cardinal splines have the same degree of accuracy, with smaller support and lower polynomial degree. Therefore, the presented splines are expected to lead to a significant reduction of the computation time and storage space.
For the entire collection see [Zbl 1024.00029].


94A12 Signal theory (characterization, reconstruction, filtering, etc.)
41A15 Spline approximation