This work outlines the development of a multi-pinhole SPECT system designed to produce a synthetic-collimator image of a small field of view. The focused multi-pinhole collimator was constructed using rapid-prototyping and casting techniques. The collimator projects the field of view through forty-six pinholes when the detector is adjacent to the collimator. The detector is then moved further from the collimator to increase the magnification of the system. The amount of pinhole-projection overlap increases with the system magnification. There is no rotation in the system; a single tomographic angle is used in each system configuration. The maximum-likelihood expectation-maximization (MLEM) algorithm is implemented on graphics processing units to reconstruct the object in the field of view. Iterative reconstruction algorithms, such as MLEM, require an accurate model of the system response. For each system magnification, a sparsely-sampled system response is measured by translating a point source through a grid encompassing the field of view. The pinhole projections are individually identified and associated with their respective apertures. A 2D elliptical Gaussian model is applied to the pinhole projections on the detector. These coeficients are associated with the object-space location of the point source, and afinely-sampled system matrix is interpolated. Simulations with a hot-rod phantom demonstrate the efficacy of combining low-resolution non-multiplexed data with high-resolution multiplexed data to produce high-resolution reconstructions.