Revised consistency conditions for PET data

Tomographic Data Consistency Conditions (TDCC) are frequently employed to improve the quality of PET data. However, most of these consistency conditions were derived from X-ray computerized tomography (CT) and their validity for other imaging modalities has not been well established. For instance, it is well known from (X-ray) CT data that the sum of the projection data from one view of the parallel-beam projections is a constant independent of the view-angle. This consistency condition is based on well-known mathematical properties of the Radon transform and yields good results when employed in noise removal or sinogram restoration. But this consistency condition assumes that emission and detection of radiation occur within a thin (ideally with zero width) line-of- response (LOR), with a flat probability distribution of the detection (in PET) or absorption (X-ray) along such LOR This assumption, being valid for CT, is not realistic for PET acquisitions. Thus, TDCC for PET should be revised in order to check their validity with more realistic detection models. In this work we review the main differences between PET and CT data and study whether these consistency conditions should be modified in order to take into account the dependence of the probabilities on the distance to the center of the line-of-response. Results from simulations are also presented to illustrate the importance of these effects. They indicate that some consistency conditions can be violated at the 10% level.