Theoretical Bounds and System Design for Multipinhole SPECT

The pinhole camera in single photon emission computed tomography (SPECT) has an inherent trade-off between resolution and sensitivity. Recent systems overcome this to some extent by utilizing multiple pinholes distributed around the imaging object. The present work is a theoretical study on how to optimally construct such systems. We use an analytic model to analyze the multipinhole SPECT geometry and identify the underlying trade-offs. One of the results is the derivation of the upper bound for the sensitivity, given the geometric resolution and field-of-view (FOV). Reaching this bound requires an infinitely large detector. However, a sensitivity very close to the upper bound can be achieved by a system with realistic proportions. We show that it is usually possible to get a sensitivity that is 95%-99% of the upper bound. Further analysis reveals a trade-off between sensitivity, magnification, and the number of pinholes. Based on this new theory, we develop a strategy for multipinhole SPECT design, from which a number of example systems are computed. Penetration in the pinhole knife edge is accounted for by using the resolution and sensitivity equivalent apertures.