Filters for three-dimensional limited-angle tomography

One approach to the three-dimensional, tomographic reconstruction of data from a planar dual-detector stationary positron camera necessitates frequency-space filtering of the image obtained from back-projection. It is therefore useful to have a closed-form expression for the appropriate filter, but the derivation is complicated by the fact that the camera measures only a limited angular range of projections. Nevertheless, suitable expressions can be obtained and are here derived for detectors of rectangular and circular cross-section.