On the deconvolution of exponential response functions

The deconvolution or unfolding of exponential response functions from experimental data was examined through the use of a Bayesian based algorithm. The algorithm, which is founded upon the concepts of probability, ensures positivity of solution. This constraint leads to a significant reduction in the growth of statistical noise in deconvolved data when compared with the more common linear unfolding techniques. The algorithm is an iterative procedure which, in the absence of statistical noise, can ultimately result in complete signal recovery. When noise is present, the degree with which the response function is removed must be balanced against the growth in the noise and, at some point, terminate the iterative process. Criteria for determining the point at which this 'best estimate' is attained are examined and an operationally realisable test is given. Comparison of results is made with the inverse filter solution which, for an exponential response function, is shown to consist of the sum of the observed data and its first derivative. (author)