Scatter-to-primary based scatter fractions for transmission-dependent convolution subtraction of SPECT images

In single photon emission computed tomography (SPECT), transmission-dependent convolution subtraction has been shown to be useful when correcting for scattered events. The method is based on convolution subtraction, but includes a matrix of scatter fractions instead of a global scatter fraction. The method can be extended to iteratively improve the scatter estimate, but in this note we show that this requires a modification of the theory to use scatter-to-total scatter fractions for the first iteration only and scatter-to-primary fractions thereafter. To demonstrate this, scatter correction is performed on a Monte Carlo simulated image of a point source of activity in water. The modification of the theory is compared to corrections where the scatter fractions are based on the scatter-to-total ratio, using one and ten iterations. The resulting ratios of subtracted to original counts are compared to the true scatter-to-total ratio of the simulation and the most accurate result is found for our modification of the theory.