Medical image enhancement is an effective tool to improve visual quality of digital medical images. However, conventional linear image enhancement methods often suffers from problems such as over-enhancement and noise sensitivity. In this paper, we study nonlinear arithmetic frameworks designed to solve the common problems of linear enhancement methods, namely, LIP, PLIP and GLIP. We also introduce nonlinear unsharp masking algorithms based on the logarithmic image processing models for medical image enhancement. Experiments are conducted to evaluate and compare the performance of the methods.