Bayesian analysis of signal deconvolution using measured instrument response functions

Abstract

Using measured instrumental response functions for data deconvolution is a known source of uncertainty. This problem is revisited here with Bayesian data analysis an Monte Carlo simulations. Noise correlation induced by the convolution operator is identified as a major source of uncertainty which has been neglected in previous treatments of this problem. Application to a luminescence lifetime measurement setup shows that existing approximate treatments are markedly defficient and that the correlation length of the noise is directly related to the lifetime to be estimated. Simple counteractive treatments are proposed to increase the accuracy of this procedure.