Smoothing exponential-polynomial splines for multiexponential decay data

In many applications, the definition of fitting models that mimic the behaviour of experimental data is a challenging issue. In this paper a data-driven approach to represent (multi)exponential decay data is presented. We propose a fitting model based on smoothing splines defined by means of a differential operator. To solve the linear system involved in the smoothing exponential-polynomial spline definition, the main idea is to define B-spline like functions for the spline space, that are locally represented by Bernstein-like bases through Hermite interpolation conditions.