TITLE: Pinhole SPECT with Different Data Acquisition Geometries: Usefulness of Unified Projection Operators in Homogeneous Coordinates


AUTHORS: Yuchuan Wang, Benjamin Tsui



PURPOSE: To further improve pinhole SPECT imaging, we develop an efficient framework for studying the reconstruction and geometric calibration problems presented due to the use of nonstandard collimator designs and/or acquisition geometries.


METHODS AND MATERIALS: Homogeneous coordinates provide a compact and convenient framework to unify the geometric descriptions of the projection operators for different imaging geometries, which may facilitate the implementation of iterative reconstruction algorithms and the investigation of crucial geometric calibration problems in pinhole SPECT. They form a natural basis for unconventional imaging geometries to project a 3D object onto a 2D imaging plane. The projection process can be represented by multiplications of a series of 4 by 4 matrices, which provides a convenient geometric "lookup table" for implementing a voxel-driven projector/backprojector pair - a foundation for implementing image reconstruction algorithms. In this work, these advantages were demonstrated through three examples, namely, multi-pinhole SPECT, pinhole SPECT with a helical scanning orbit, and pinhole SPECT with dual detectors. Experimental studies were performed to demonstrate the validity of our approaches.



RESULTS: 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 multi and single pinhole projection operators allowed us to derive that one can accurately calibrate a multi-pinhole geometry using only two point sources without measuring their distance.





CONCLUSIONS: We described various pinhole SPECT imaging geometries using homogeneous coordinates, and successfully developed and implemented iterative OS-EM reconstruction methods for projection data acquired from these geometries. This contributes to not only ease of software implementation, but greater flexibility in adapting the process to new or modified data acquisition geometries. This approach can be easily adapted for use with other novel imaging geometries in SPECT and cone-beam x-ray CT. 


  Homogeneous coordinates are useful in describing different pinhole SPECT data acquisition geometries and can greatly reduced the time needed for developing and implementing iterative image reconstruction algorithms.  It is also beneficial for unifying geometric calibration methods and facilitating the discovery of solutions to geometric specific problems.