Multiple-pinhole transaxial tomography: A model and analysis.

Abstract

Multiple-pinhole transaxial tomography, a form of single-photon emission computed tomography (SPECT), is performed using novel imagers that have arrays of pinholes for image formation rather than collimators. Some such imagers, the University of Arizona (UA) transaxial systems, consist of coded apertures and modular gamma cameras and acquire data without system motion. They are the only such SPECT systems. This dissertation presents results from studies in which tomography using the UA imagers was simulated and studies in which the singular-value decompositions (SVDs) of multiple-pinhole imagers were calculated. The studies were performed to assess system configurations and to begin characterization of multiple-pinhole tomographs in terms of their SVDs. Our initial study involved simulation of systems consisting of arrays with uniformly spaced pinholes that produce multiplexed data and polygonal detectors comprising sixteen UA modules. This study shows that useful images can be obtained from static systems that have apertures that produce duplexed data and that significantly more useful images can be obtained using detectors that have resolution that is twice as fine as that of the UA modules. Numerical computation of the SVDs of several imagers including a single-pinhole imager and an orthogonal-pinhole imager produced visual displays of the object-space singular vectors of the systems. These displays demonstrate that the SVDs of multiple-pinhole systems can be expressed in terms of the SVDs of single-pinhole systems. The symmetries of all single-slice systems are rotational or reflective. The associated symmetry groups are cyclic groups or dihedral groups. The object-space singular vectors of these systems exhibit the same symmetries as the systems and exhibit multiplicities consistent with the irreducible representations of the associated groups. Results of analysis of the calculated SVDs demonstrate relationships among system symmetries, singular-vector symmetries, and irreducible representations. The results of our final study, a comparison of a system that has 64 pinholes spaced uniformly with one that has 64 pinholes spaced as a dilute uniformly redundant array, show that systems that have pinholes that are not uniformly spaced may prove the most useful.