Two proposed likelihood models for emission and transmission image reconstruction accurately incorporate the Poisson nature of photon counting noise and a number of other relevant physical features. As in most algebraic schemes, the region to be reconstructed is divided into small pixels. For each pixel a concentration or attenuation coefficient must be estimated. In the maximum likelihood approach these parameters are estimated by maximizing the likelihood (probability of the observations). EM algorithms are iterative techniques for finding maximum likeihood estimates. The general principles behind all EM algorithms and the specific algorithms for emission and transmission tomography are examined in dental. The virtues of the EM algorithms include accurate incorporation of a good physical model, automatic inclusion of non-negativity constraints on all parameters, an excellent measure of the quality of a reconstruction and global convergence to a single vector of parameter estimates. The specification of necessary physical features such as source and detector geometries are discussed. Actual reconstructions are deferred to a later time.