An investigation of noise characteristics in OSEM reconstruction of fan beam SPECT using a rotating/warping projector/backprojector

The improved detection efficiency/resolution tradeoff inherent in fan-beam collimators may be used to provide better counting statistics for SPECT imaging and should result in better noise characteristics in the reconstructed image as compared to parallel hole collimators for a given resolution. It has previously been observed for fan-beam filtered backprojection that it is important to backproject projection bins into all image pixels from which they can geometrically record counts. Previous implementations of iterative reconstruction using a rotating/warping projector/backprojector have also not demonstrated the expected improved in noise properties. We hypothesized that this was due to a mismatch in the implicit projector/backprojector system matrices brought about by the use of simple two-bin linear interpolation in the backprojector. The solution proposed here is to convolve each row in the backprojection image parallel to the collimator face with a summing kernel of length equal to the magnification factor for that row distance prior to unwarping and rotating. This convolution results in inclusion of the contribution from each detector bin to the appropriate image voxel. We demonstrate that the use of the summing kernel reduces the mismatch between the projector and backprojector and results in improved noise properties for fan-beam versus parallel hole reconstructions as a function of iteration. However, the use of the summing kernel results in slower resolution recovery and a poorer noise-resolution tradeoff.