Positron emission tomography (PET) is based on the detection of pairs of photons emitted by a positron emitting radioactive tracer administered to the patient. Reconstruction algorithms process these emission data to estimate the spatial distribution of the tracer in the body. These algorithms require information on the tissue density to correct for the photon attenuation within the patient. Multi-modality PET/CT systems obtain the tissue density from the CT image, but this procedure is inaccurate when patient motion occurs between the PET and the CT scans or when the attenuation image derived from CT is incomplete. Similar problems occur with PET/MR systems. This project aims at reconstructing the radioactive tracer distribution and the tissue density from the emission data without using CT or MR; this ensures that the tissue density used for reconstruction spatially and temporally matches the emission data. Our approach applies to the time-of-flight (TOF) PET systems, which measure with an accuracy of about 400-600 ps the difference between the detection times of the two photons. The project builds on preliminary results, including the proof that the simultaneous problem has a unique solution in 2D TOF-PET, promising results with an iterative algorithm, and the use of additional radioactive sources placed around the patient. Improved algorithms will be developed, optimal configurations of the sources will be identified, and the methods will be applied to PET/CT and PET/MR.