Simultaneous maximum a posteriori reconstruction of attenuation and activity distributions from emission sinograms

In order to perform attenuation correction in emission tomography an attenu ation map is required. We propose a new method to compute this map directly from the emission sinogram, eliminating the transmission scan from the acq uisition protocol. The problem is formulated as an optimization task where the objective function is a combination of the likelihood and an a priori p robability. The latter uses a Gibbs prior distribution to encourage local s moothness and a multimodal distribution for the attenuation coefficients. S ince the attenuation process is different in positron emission tomography ( PET) and single photon emission tomography (SPECT), a separate algorithm fo r each case is derived, The method has been tested on mathematical phantoms and on a few clinical studies. For PET, good agreement was found between t he images obtained with transmission measurements and those produced by the new algorithm in an abdominal study. For SPECT, promising simulation resul ts have been obtained for nonhomogeneous attenuation due to the presence of the lungs.