A mathematical formulation of the single-pinhole transform and asymptotic properties in fourier space

The recent introduction of organ specific imaging systems such as the GE Discovery NM 530c has focused attention on using arrays of small cameras using single-pinhole collimators. While offering advantages in terms of the speed of data acquisition and detection sensitivity, cost issues arise with an increased number of detectors. The goal of this research is to minimize the number of detectors for data acquisition while preserving the resolution of the reconstructed images so that small structures of interest can be reconstructed reliably. The approach taken to solve this problem is to analyze the Fourier properties of a mathematical formulation of the single-pinhole transform in order to construct an optimal sampling lattice. The sampling lattice, in turn, dictates the distance between pinholes and the shift of the detector surface if required.