On the deconvolution of exponential response functions

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Abstract
The deconvolution or unfolding of exponential response functions from experimetnal data was examined through the use of a Bayesian theorem-based algorithm. The algorithm, which is founded on 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 one must balance the degree with which the response function is removed 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 realizable 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 1st derivative.