PET (positron emission tomography) scans are still in the experimental phase, as one of the newest breast cancer diagnostic techniques. There are two traditional approaches to the computation of images from data collected in PET. In the first, standard CT (computed tomography) algorithms are used on rays designated by pairs of detectors receiving coincidence events. The problem generated by this approach is that generally only the mean can be used by such algorithms. With the relatively small numbers of events in PET, and with Poisson statistics for which variance equals the mean, the noise sensivity of standard CT algorithms becomes limiting. This is exasperated further by 3D imaging with cylindrical arrays of detectors. Statistical CT algorithms take the variance into account. As in the list-mode approach, we consider each coincidence event individually. However, we estimate the location of the annihilation event that caused each coincidence event, one by one, based on the previously assigned location of events processed earlier. The estimated annihilation locations form the image. To accomplish this, we construct a probability distribution along each coincidence line. This is generated from previous annihilation points by density estimation. In this paper we present our density estimation approach to positron emission tomography. Nonparametric methods of density estimation are overviewed followed by numerical examples. Our goal here is to determine which density estimation approach is most suitable for PET.