Quantitative image reconstruction in positron emission tomography requires attenuation correction. In case the attenuation correction is not measured separately, under certain conditions this can be determined from the emission data alone. We present a method based on cluster analysis that assumes only 3 empirical attenuation coefficients, i.e., 0.095 cm-1 for soft tissue, 0.02 cm-1 for lung, and 0 cm-1 for air. The subsequent image reconstruction takes place in an iterative fashion, through maximization of image likelihood. For the mathematical thorax phantom used in the present study, the results are comparable to those obtained after separate measurement of the attenuation correction.