Activity and Attenuation Reconstruction for Positron Emission Tomography Using Emission Data Only Via Maximum Likelihood and Iterative Data Refinement

Emission computed tomography reconstruction requires compensation for photon attenuation. The usual way to do this is by performing a 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 that consists of a combination of a minorizing function algorithm applied to the likelihood function plus the application of an appropriate decreasing multiplicative factor and iterative data refinement. We compare this new approach with previous ones and our simulations show very encouraging results as far as solving the `crosstalk´ problem is concerned