Modeling the distance-dependent blurring in transmission imaging in the ordered-subset transmission (OSTR) algorithm by using an unmatched projector/backprojector pair

In SPECT, accurate emission reconstruction requires attenuation compensation with high-quality attenuation maps. Resolution loss in transmission maps could cause blurring and artifacts in emission reconstruction. For a transmission system employing parallel-hole collimators and a sheet source, distance-dependent blurring is caused by the non-ideal source and camera collimations, and the finite intrinsic resolution of the detector. These can be approximately modeled by an incremental-blurring model. To compensate for this blurring in iterative transmission reconstruction, we incorporated the incremental blurring model in the forward projector of the OSTR algorithm but did not include the blur in the backprojector. To evaluate our approach, we simulated transmission projections of the MCAT phantom using a ray-tracing projector, in which the rays coming out from a source point form a narrow cone. The geometric blurring due to the non-ideal source and camera collimations was simulated by multiplying the counts along each cone-beam ray with a weight calculated from the overall geometric response function (assumed a two-dimensional Gaussian function), and then summing the weighted counts into projections. The resulting projections were convolved with the intrinsic response (another two-dimensional Gaussian) to simulate the total system blurring of transmission imaging. Poisson noise was then added to the projection data. We also acquired two sets of transmission measurements of an air-filled Data Spectrum Deluxe SPECT phantom on a Prism 2000 scanning-line-source transmission system. We reconstructed the simulations using the OSTR algorithm, with and without modeling of the incremental blur in the projector. The scaling parameter of the penalty prior was optimized in each case by minimizing the root-mean-square error (RMSE). Reconstructions showed that modeling the incremental blur improved the resolution of the attenuation map and quantitative accuracy