Spline approximation: 2D reconstruction by optimal quasi-interpolation on Cartesian and hexagonal lattices.
Laurent Condat, Institut National Polytechnique de Grenoble, Grenoble, France

Seminar • 23 November 2005 • BM 4.235

Abstract
It is often required to modelize discrete signals by a continuously-defined function, e.g. for resampling purpose. This discrete-to-continuous conversion can be interpreted as a reconstruction problem: given discrete samples of an unknown function, we try to approximate it in a functional space like a spline space. The classical consistent solution consists in choosing the spline that interpolates the data. This solution is not optimal from an approximation theoretic point of view, and quasi-interpolation is often a better alternative. I will show how to design optimal prefilters that give better results in concrete applications like image rotation, hexagonal-to-Cartesian resampling, and demosaicking.