Estimating crystal growth rates using computed tomography

It has been observed that sugar crystals growing in solution exhibit growth rate dispersion, that is, variation in growth rate from one crystal to the next. We consider the problem of estimating the distribution of growth rates in batch-grown crystals, given only samples of their sizes at a number of fixed points in time. The problem can be expressed as a tomographic image reconstruction problem, in which we try to reconstruct the joint density of initial size and growth from a set of marginal densities obtained by integrating the joint density in a number of different directions