High accuracy deconvolution method using spline functions

A spline-based deconvolution method for use with experimentally derived data is presented. The method is based on the fact that for a not too wide resolution function, if the original function is a piece-wise cubic, so is the convoluted function. The two functions have the same knots and their coefficients are related by a set of simple equations, so that once the values of the convoluted function, measured in the laboratory, are fitted by a piece-wise cubic spline and its coefficient are obtained, one is able to calculate the coefficients of the cubic function representing the desired, deconvoluted function. The novel features of the method, including the influence of the width of the resolution function, are fully discussed and results of its application to simulated data are presented. Results obtained for the same data with two other widely used deconvolution methods are also presented and the comparative merits and demerits of the methods are discussed. Our method proves to be stable and accurate, and to yield high quality results even in difficult cases with which the two other methods are unable to cope successfully.