Spatial resolution in computed tomography (CT) has been limited because of the excessive increases in statistical noise associated with increasing resolution. Reconstruction filter functions have been designed to produce tomographic images with resolution as close as possible to the intrinsic detector resolution. Since these filter functions apply an increasing weight to increasing spatial frequencies in the measured data, this produces a large amplification of noise at the upper end of the spatial frequency band of the filter function where the signal from the detector has a low amplitude. This mathematical approach to spatial frequency amplification cannot distinguish between signal and noise and thus both are amplified equally. An approach for improving tomographic resolution is the use of very small detectors to selectively amplify the signal but not noise. This signal amplification technique (SAT) can provide improvements in image resolution without increases in the cutoff frequency of the reconstruction algorithm. Alternatively, in cases in which image counts are low, statistical noise can be reduced by lowering the cutoff frequency. A possible system design for a positron CT system with SAT is described.