A simple model for the efficient correction of collimator blur in 3D SPECT imaging

The problem of performing an efficient compensation of collimator blur in the three-dimensional (3D) reconstruction of SPECT data acquired in parallel beam geometry is tackled. An approximate model for data acquisition is developed, which leads to the construction of the corresponding projector-backprojector pair. In order to perform some numerical tests, the model is customized to a state-of-the-art neuro-SPECT scanner, which is supplied with a three-segmented parallel beam collimator. Some reconstruction algorithms based on this customization are presented and their results are compared, in terms of quality and timing requirements, with the outcome generated by the corresponding fully 3D model. According to this numerical simulation, where voxel-driven (back-)projectors are used, the conclusion can be drawn that the approximate model produces reconstructions as good as the ones generated by the fully 3D model in a time which is one order of magnitude shorter. In the case that (back-)projectors based on the rotation of the emission matrix are used, the proposed approximate model is evaluated to be about four times faster than the corresponding fully 3D model.