In medical imaging applications, the expectation maximization (EM) algorithm is a popular technique for obtaining the maximum likelihood estimate (MLE) of the solution to the inverse imaging problem. The Richardson/Lucy (RL) method, derived under different assumptions, is identical to this particular EM algorithm. The RL method is commonly used by astronomers in image deconvolution problems from astronomical data. A closely related algorithm, which we shall refer to as the Poisson MLE, was proposed recently in the context of image superresolution. These algorithms can be grouped under minimum Kullback-Leibler distance methods (minimum cross-entropy methods) as opposed to the standard least-squares methods. The purpose of this paper is twofold. In the first part we explore a common underlying conceptual similarity in the algorithms, even though they were derived under varying assumptions. In the second part, we empirically evaluate the performance of this class of algorithms via experiments on simulated objects, for the image superresolution problem. One set of experiments examines the data consistency performance of the algorithms. A second set of experiments evaluates the performance on the addition of simple constraints on the estimate.