Maximum entropy is applied to the problem of reconstructing nuclear medicine images. The physics of the formation of these images is reviewed showing a number of phenomena which degrade both two and three dimensional estimates of tracer distribution. The development and theoretical justification of maximum entropy as an image processing technique is also discussed. Maximum entropy is then applied to the problem of image reconstruction in a series of approximations. Firstly, a single planar nuclear medicine image is modelled as a convolution of a two dimensional distribution with a point-spread-function. Maximum entropy deconvolution is described and applied to the problem of restoring the blur free distribution. This technique improves image quality assessed by a number of criteria. A second, more accurate model of the planar imaging process is developed: blurring effects are modelled to depend on the source to camera distance. The planar image is considered a weighted sum of a series of convolutions with different point spread functions. Simultaneously acquired opposed views are considered and from these, a three dimensional distribution reconstructed. A weighted projection of this distribution appears a better planar representation of the distribution than solutions found by the previous method. Finally, the full three dimensional distribution is reconstructed from a series of views. The effects of attenuation collimator response and scatter on the projections are approximately modelled. The attenuation coefficient is considered to be constant inside the surface of the object to be reconstructed. Blurring effects due to collimator and scatter are considered to depend only on the distance between source and camera.