Pinhole SPECT with different data acquisition geometries: Usefulness of unified projection operators in homogeneous coordinates

To further improve pinhole single photon emission computed tomography (SPECT) imaging, there have been increasing interests in the use of nonstandard collimator designs and/or acquisition geometries. Homogeneous coordinates provide a compact and convenient framework to unify the geometric descriptions of the projection operators for these different imaging geometries, which may facilitate the implementation of iterative reconstruction algorithms and the investigation of crucial geometric calibration problems in pinhole SPECT. In this work, these advantages were demonstrated through three examples, namely, multipinhole SPECT, pinhole SPECT with a helical scanning orbit, and pinhole SPECT with dual detectors. Specifically, we showed adaptable implementations of iterative image reconstruction algorithms and translatable strategies for efficient geometric calibrations through unifying projection operators of the aforementioned imaging geometries. Notably, the unified geometric descriptions of multipinhole and single pinhole projection operators allowed us to derive that one can effectively calibrate a multipinhole geometry using only two point sources without measuring their distance. Experimental studies were performed to demonstrate the validity of our approaches, which may be extended to other pinhole SPECT and cone-beam X-ray computed tomography imaging geometries.