Scatter estimation scaling with all count use by employing discrete Data Consistency Conditions

A typical PET acquisition does not separate true coincidence events from scatter because of poor energy resolution. The Single Scatter Simulation (SSS) is used to estimate scatter distribution sequentially with emission activity image reconstruction. Due to unknown activity outside the field of view and approximation in the SSS itself, scatter distribution is scaled to measure data in a sinogram region where true activity projection is known to be zero. Such a region typically contains a small number of counts and tail of scatter distribution and this can result in errors in the scaling parameter estimation. In this work we present a method to scale known scatter distribution to measured data in regions where contributions from truly coincidence emission images can be expected. In other words, all counts are used in the scatter scaling problem. We explore a constraint where true coincidence sinogram distribution must be a projection of some activity image, the Data Consistency Conditions. An iterative algorithm is presented that reconstructs the emission image from available counts. Scatter scaling estimation is a by-product of this reconstruction. Initial results show that scaling parameters can be estimated in regions where both scatter and true coincidence events coexist.