Simultaneous activity attenuation reconstruction in positron emission tomography via maximum likelihood and iterative methods

Emission computed tomography reconstruction requires compensation for photon attenuation. The usual way to do this is by a previous transmission scan to reconstruct the attenuation map. An important improvement could be achieved if it is possible to retrieve the attenuation map directly from the activity data. Several approaches have been suggested before to do this by using iterative methods for solving maximum likelihood (ML) problems (or penalized maximum likelihood, MAP) that take into account the Poisson nature of the noise. One of the main drawbacks has been that these methods tend to retrieve solutions that generate an undesired crosstalk between the attenuation and the activity maps. In this paper we present a new approach to the problem in positron emission tomography that uses a minorization function algorithm applied to the Poisson likelihood function; this algorithm, together with an appropriate decreasing multiplicative factor and iterative data refinement tend to eliminate the crosstalk between the images.