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About six years ago, it was shown with experiments and with mathematical analysis that with the introduction of time-of-flight (TOF), the data acquired with positron emission tomography (PET) were significantly richer than before 1-3. In particular, it was found that if the tracer distribution is wider than the TOF uncertainty, the TOF-PET data provide enough information to jointly estimate the activity image and the attenuation sinogram up to a global scale factor. Since then, many algorithms have been proposed to exploit this feature to perform attenuation correction without additional transmission measurements or to improve available attenuation images or sinograms. An excellent recent review of these methods has been published by Berker and Li 4. Some of these methods rely on the emission data only, other methods use additional information to determine the scale factor and/or to suppress noise propagation. This additional information can be obtained from an anatomical image acquired with the MR-component in a PET/MR system or with the CT-component in a PET/CT system.
Nuyts et al. (Sun,) studied this question.