The convolution scatter subtraction hypothesis and its validity domain in radioisotope imaging

The additive degradation model assumes that the measured projection data is the sum of scatter and primary distributions. Within this framework, the scatter projection can be estimated by convolving the primary projection with a point or line response function normalized to primary. The convolution scatter-subtraction was formulated to overcome the fact that the primary projection is not available for such estimation. This hypothesis assumes that accurate scatter projection data can be obtained by convolving the measured projection (which is readily available) with scatter response function normalized to primary plus scattered events. The aims of this work are (i) to investigate the truth of this assumption and (ii) to delineate its validity domain. The authors have found that the assumption is valid if relatively large matrices are used to accommodate all the values of the scatter response functions. This requirement is particularly critical when imaging large objects using large discrimination windows. The validity of the assumption rapidly deteriorates as the measured projections change from smooth to diffuse distributions. At this point, the shapes of scatter response functions become important.