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

The problem of performing an efficient compensation of collimator blur in t he three-dimensional (3D) reconstruction of SPECT data acquired in parallel beam geometry is tackled. An approximate model for data acquisition is dev eloped, which leads to thr construction of the corresponding projector-back projector pair. In order to perform some numerical tests, the model is cust omized to a state-of-the-art neuro-SPECT scanner, which is supplied with a three-segmented parallel beam collimator. Some reconstruction algorithms ba sed 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, wher e voxel-driven (back-)projectors are used, the conclusion can be drawn that the approximate model produces reconstructions as good as the ones generat ed 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 m atrix are used, the proposed approximate model is evaluated to be about fou r times faster than the corresponding fully 3D model.