Oversampled filters for quantitative volumetric PET reconstruction

Three-dimensional filtered backprojection uses filters generally specified in the Fourier domain. Implementing these filters by direct sampling in the Fourier domain produces an artifact in the reconstructed images consisting primarily of a DC shift. This artifact is caused by aliasing of the reconstruction filter. The authors have developed a filter construction technique using Fourier domain oversampling, which reduces the artifact. A method to construct the filter efficiently without the need to create and store the entire oversampled filter array is also presented. Quantitative accuracy in filtered backprojection is of particular importance in multiple-pass algorithms used to reconstruct data from cylindrical PET scanners. The authors are able to implement such algorithms without fitting the reprojected views to the scanner data.