In vivo dose localization in light ion tumour therapy can be performed by measuring the range distributions of beta+ active ions in tissue employing positron emission tomographic techniques. For this purpose a multiplicative iteration scheme for reconstructing three-dimensional images from shift-variant, limited-angle data is presented. In the iterative correction steps the algorithm uses the geometric means of quotients calculated from the three-dimensional Radon transforms of the backprojected measured and approximated source distributions. When sources measured with poor statistics are reconstructed, an effective noise suppression is achieved.