A smoothed em algorithm for the solution of wicksell's corpuscle problem

Abstract

In this paper a new method called the EMS algorithm is used to solve Wicksell's corpuscle problem, that is the determination of the distribution of the sphere radii in a medium given the radii of their profiles in a random slice. The EMS algorithm combines the EM algorithm, a procedure for obtaining maximum likelihood estimates of parameters from incomplete data, with simple smoothing. The method is tested on simulated data from three different sphere radii densities, namely a bimodal mixture of Normals, a Weibull and a Normal. The effect of varying the level of smoothing, the number of classes in which the data is binned and the number of classes for which the estimated density is evaluated, is investigated. Comparisons are made between these results and those obtained by others in this field.