The use of a NPWMF observer to compare 3D NEC-OSEM FORE + 2D NEC-OSEM in whole-body PET

The Fourier Rebinning (FORE), which sorts 3D data into 2D data, requires that the 3D sinogram is previously corrected for non-quantitative physical effects. So, 2D sinograms are no longer Poisson distributed, an assumption behind OSEM (Ordered Subsets Expectation Maximization). This means that whenever data are corrected and OSEM is the reconstruction algorithm, the need to restore the Poisson characteristics is present. The NECtransformation method, whose principle is to transform the input data to their noise equivalent counts (NEC) such that the two first moments of the transformed data are equal, is a way to achieve that restoring. This is done either by weighting the input sinogram (p) by the ratio of its mean to its variance (NEC-scaling): ) ( 2 p p w σ = , or by adding to the data a factor which is equal to the difference between its variance and its mean (NEC-shifting): p p − ) g = ( 2 σ . The effects of all corrections, including FORE if used, are taken into account in the model for the variance. NEC-scaled data was used as input for the weighted OSEM, in both 2D and 3D cases: