Computationally efficient collimator-detector response compensation in high energy SPECT using 1D convolutions and rotations

<i>Objective</i>. Modeling of the collimator-detector response (CDR) in single photon emission computed tomography (SPECT) reconstruction enables improved resolution and accuracy, and is thus important for quantitative imaging applications such as dosimetry. The implementation of CDR modeling, however, can become a computational bottleneck when there are substantial components of septal penetration and scatter in the acquired data, since a direct convolution-based approach requires large 2D kernels. This work proposes a 1D convolution and rotation-based CDR model that reduces reconstruction times but maintains consistency with models that employ 2D convolutions. To enable open-source development and use of these models in image reconstruction, we release a SPECTPSFToolbox repository for the PyTomography project on GitHub.<i>Approach</i>. A 1D/rotation-based CDR model was formulated and subsequently fit to Monte Carlo (MC) point source data representative of¹⁷⁷Lu,¹³¹I, and²²⁵Ac imaging. Computation times of (i) the proposed 1D/rotation-based model and (ii) a traditional model that uses 2D convolutions were compared for typical SPECT matrix sizes. Both CDR models were then used in the reconstruction of MC, physical phantom, and patient data; the models were compared by quantifying total counts in hot regions of interest (ROIs) and activity contrast between hot ROIs and background regions.<i>Results</i>. For typical matrix sizes in SPECT reconstruction, application of the 1D/rotation-based model provides a two-fold computational speed-up over the 2D model when running on GPU. Only small differences between the 1D/rotation-based and 2D models (order of 1%) were obtained for count and contrast quantification in select ROIs.<i>Significance</i>. A technique for CDR modeling in SPECT was proposed that (i) significantly speeds up reconstruction times, and (ii) yields nearly identical reconstructions to traditional 2D convolution based CDR techniques. The released toolbox will permit open-source development of similar models for different isotopes and collimators.