Statistical procedure for deconvoluting experimental data

Abstract

A general procedure of the deconvolution of noisy experimental data is proposed. The deconvoluted solution is represented in terms of a cubic spline function f(x) with variable knots. The value of parameters and the location of knot points in the spline are determined by solving the nonlinear least-squares problem of fitting g(x)=∫κ(τ)f(s(τ,x))dτ to the data, where experimental data g(x) represent the convolution of f[s(τ,x)] with an apparatus weighting function k(τ) and s(τ,x) is a function related to the configuration of the experimental system. The profile of the fitted solution varies widely with different choices of the number and position of knots in the spline. To obtain a good solution, the optimum number of knots is determined based on the data by applying minimum Akaike’s Information Criterion procedure. Practical application of the variable-knot spline is generally considered to be rather intricate. However, by taking advantage of an advanced technique of a quasi-Newton method, the nonlinear least-squares problem becomes tractable, and excellent smoothing in the deconvoluted solution can be achieved.