A filtering technique to compensate for detector response in converging-beam SPECT reconstruction

A nonstationary filtering technique was developed to compensate for spatially variant detector response in fan- and cone-beam SPECT. First the frequency-distance relation for fan- and cone-beam geometries was derived from their parallel-beam counterpart, and then used to compute the Fourier transform of the detector response that was used as the MTF of a Metz filter. The filter was applied to the blurred data before reconstruction. The unique feature of the derived MTF is that it depends on source location, so the filtering is spatially variant. Results of evaluation studies demonstrate that the ratio between the tangential and radial FWHMS of the reconstructed point response function obtained from the authors' filtering technique is closer to one and varies less with source location as compared to the ratio obtained without compensation or using Metz filtering with a stationary detector response. This improvement is mainly because the tangential FWHM is increased to match the radial FWHM better. With a higher order of Metz filter, both tangential and radial FWHMS are slightly smaller but their ratio deviates more from one compared to those of lower orders. In conclusion, the authors' filtering technique provides an effective means to compensate for detector response mainly in terms of reducing anisotropy of the point response function.