Bayesian deconvolution II: Noise properties

Abstract

In the second of a series of communiqués regarding a deconvolution algorithm based upon Bayes' postulate the question of statistical noise magnification is examined. The method, being non-linear, makes noise analysis more difficult than that commonly encountered in linear methods. Explicit expressions have been derived for noise growth as a function of both the iteration index and the response function. Comparison of resolution enhancement to noise growth between Van Cittert's linear method and the Bayesian approach revealed that a very significant improvement is obtained with the latter. Detailed analysis of the nature of noise growth, and the characteristic pattern, is reported for the Bayesian algorithm. The effect of the inherent positivity constraint is also examined. For symmetric response functions it is shown that centroid information is retained during the deconvolution operation. The work reported here clearly shows noise growth can be effectively controlled while very significant improvement in resolution is attained.