Statistical optimality of Hermite splines for the reconstruction of self-similar signalsMS47

Hermite splines are commonly used for interpolating data when samples of the derivative are available, in a scheme called Hermite interpolation. Assuming a suitable statistical model, we demonstrate that this method is optimal for reconstructing random signals in Papoulis’ generalized sampling framework. More precisely, we show the equivalence between cubic Hermite interpolation and the linear minimum mean-square error (LMMSE) estimation of a second-order Lévy process.

This presentation is part of Minisymposium “MS47 - Splines in Imaging (3 parts)
organized by: Carolina Beccari (Dept. Mathematics, University of Bologna) , Virginie Uhlmann (EPFL, Lausanne) , Michael Unser (EPFL, Lausanne) .

Virginie Uhlmann (EPFL, Lausanne)
approximation theory, stochastic processes